Inclusion Criteria:

* Pre-Registration - Inclusion Criteria Specific to Dose Escalation Cohort
* Histolopathological and/or molecular confirmation of either glioblastoma, IDH wildtype (GBM), (as defined by either the 2016 or 2021 World Health Organization \[WHO\] classifications) anaplastic astrocytoma, IDH wildtype (AA) (as defined by the 2016 WHO classification) or non-small cell lung cancer (NSCLC)
* EGFR Status:

* GBM/AA must either EGFR amplification and/or any activating EGFR mutation (e.g. A289T, EGFRvIII , etc.)
* NSCLC must have a confirmed activating EGFR mutation (e.g. Del19, L858R, EGFRvIII, G719A, L861Q, T790M, C797S, etc.)
* Pre-Registration - Inclusion Criteria Specific to Dose Expansion Cohorts
* Glioblastoma, IDH wildtype/Anaplastic astrocytoma, IDH wildtype (GBM/AA) Cohort:

* Diagnosis: Histological or molecular confirmation of either glioblastoma, IDH wildtype (GBM) (as defined by either the 2016 or 2021 WHO classifications) or anaplastic astrocytoma, IDH wildtype (AA) (as defined by the 2016 WHO classification)
* EGFR status: GBM/AA must have EGFRvIII mutation
* Brain Tumor Penetration (BTP) Cohort:

* Diagnosis: Histopathological or molecular confirmation of either glioblastoma, IDH wildtype (GBM) (as defined by either the 2016 or 2021 WHO classifications) or anaplastic astrocytoma, IDH wildtype (AA) (as defined by the 2016 WHO classification)
* EGFR status: GBM/AA must have been previously demonstrated to have either EGFR amplification and/or any activating EGFR mutation based on any prior resection
* Non-Small Cell Lung Cancer (NSCLC) cohort:

* Diagnosis: Histological confirmation of non-small cell lung cancer (NSCLC) ? EGFR status: NSCLC must have confirmed activating EGFR mutation
* Registration -Inclusion Criteria Specific to Dose Escalation Cohort
* Previous treatments:

* Patients with GBM/AA must have been previously treated with radiation and temozolomide
* Patients with NSCLC must have been previously treated with at least one line of single-agent therapy with an EGFR TKI e.g. gefitinib, erlotinib, afatinib, or osimertinib)
* Radiographic progression:

* Patients with GBM/AA must have radiographic progression based on RANO criteria
* Patients with NSCLC must have new or radiographic progression in the central nervous system (brain metastases and/or leptomeningeal metastases). Positive confirmation of CSF cytology is both necessary and sufficient to define the presence of leptomeningeal metastases for patients in this study. Patients with positive CSF cytology and brain metastases will be categorized as "leptomeningeal metastases."
* Measurable disease
* Eastern Cooperative Oncology Group (ECOG) 0 or 1. For patients with NSCLC with leptomeningeal metastases, ECOG 2 is also acceptable
* Registration - Inclusion Criteria Specific to Dose Expansion Cohorts
* Glioblastoma, IDH wildtype/Anaplastic astrocytoma, IDH wildtype (GBM/AA) Cohort:

* Previous treatments: Patients must have been previously treated with radiation and temozolomide. First recurrence only (no additional systemic therapies have been administered for recurrent disease)
* Radiographic progression: Patients with GBM/AA must have radiographic progression based on RANO criteria
* Measurable disease
* Performance status: ECOG 0 or 1 for patients with GBM/AA
* Brain Tumor Penetration (BTP) Cohort:

* Previous treatments: Patients must have been previously treated with radiation and temozolomide
* Radiographic progression: Patients with GBM/AA must have radiographic progression based on RANO criteria
* Therapeutic surgical resection of GBM/AA required as part of routine clinical care
* Performance status: ECOG 0 or 1
* Non-Small Cell Lung Cancer (NSCLC) cohort:

* Previous treatments: No limitations
* Radiographic progression: Patients must have new or radiographic progression in the central nervous system (brain metastases and/or leptomeningeal metastases). Positive confirmation of CSF cytology is both necessary and sufficient to define the presence of leptomeningeal metastases for patients in this study. Patients with positive CSF cytology and brain metastases will be categorized as "leptomeningeal metastases."
* Measurable Disease
* Performance Status: ECOG 0 or 1
* Registration - Inclusion Criteria Common to Dose Escalation and Dose Expansion Cohorts:
* Age \>= 18 years old
* Ability to understand and the willingness to sign a written informed consent document
* Hemoglobin \>= 9.0 g/dL (obtained =\< 14 days prior to registration)
* Leukocytes \>= 3.0 x 10\^9/L (obtained =\< 14 days prior to registration)
* Absolute neutrophil count \>= 1.5 x 10\^9/L (obtained =\< 14 days prior to registration)
* Platelets \>= 100 x 10\^9/L (obtained =\< 14 days prior to registration)
* International normalized ratio (INR) =\< 1.5 x upper limit of normal (ULN) (obtained =\< 14 days prior to registration)

* Patients on a stable dose of anti-coagulation therapy will be allowed to participate if they have no signs of bleeding or clotting and the INR/prothrombin time (PT) and partial thromboplastin time (PTT)/activated (a)PTT results are compatible with an acceptable risk-benefit ratio as per the investigator's discretion
* aPTT =\< 1.5 x ULN (obtained =\< 14 days prior to registration)

* Patients on a stable dose of anti-coagulation therapy will be allowed to participate if they have no signs of bleeding or clotting and the INR/PT and PTT/aPTT results are compatible with an acceptable risk-benefit ratio as per the investigator's discretion
* Total bilirubin =\< 1.5 x ULN and =\< 3 mg/dL for patients with Gilbert's disease (obtained =\< 14 days prior to registration)
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN or =\< 5 x ULN if due to liver involvement by tumor (obtained =\< 14 days prior to registration)
* Creatinine =\< 1.5 x ULN or estimated glomerular filtration rate (estimated glomerular filtration rate \[eGFR\]) \>= 60 mL/minute (obtained =\< 14 days prior to registration)
* Negative pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only
* Provision of signed and dated written informed consent prior to any study specific procedures, sampling, and analyses
* Willingness to provide mandatory blood specimens for correlative research
* Willingness to return to enrolling institution for follow-up (during the active monitoring phase of the study i.e., active treatment and clinical follow-up)
* Male and female patients of child bearing potential must be willing to use contraception, (i.e., condoms, birth control) while on study and until 3 months after the last dose of study drug is taken
* Must be willing to take light-protective measures during the study and for 2 weeks after their last dose of WSD0922-FU
* Must have a minimum life expectancy of \>= 3 months
* Must be stable on no more than 2 mg of dexamethasone (or equivalent steroids) per day. Steroid dose adjustments should be minimized during cycle 1 of therapy
* Must not take enzyme-inducing anticonvulsants treatment for at least 2 weeks prior to enrollment. Patients on enzyme-inducing anticonvulsants will be changed to non-enzyme inducing anticonvulsants
* Strong inducers and strong inhibitors of CYP3A should be discontinued at least 14 days prior to registration
* Willingness to provide mandatory tissue specimens for correlative research (BTP cohort only)

Exclusion Criteria:

* Registration - Exclusion Criteria for Dose Escalation and Dose Expansion
* Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown:

* Pregnant persons
* Nursing persons
* Persons of childbearing potential who are unwilling to employ adequate contraception
* Any of the following prior therapies:

* Any cytotoxic chemotherapy or other anticancer drugs for the treatment of advanced NSCLC from a previous treatment regimen =\< 14 days prior to registration
* In patients with NSCLC, treatment with an EGFR TKI (e.g., erlotinib, gefitinib, afatinib or osimertinib) within 8 days or approximately 5 x half-life, whichever is the longer, prior to registration (if sufficient wash-out time has not occurred due to schedule or PK properties, an alternative appropriate wash-out time based on known duration and time to reversibility of drug related adverse events could be agreed upon by the Investigator and Wayshine)
* Radiation therapy to the brain =\< 12 weeks prior to registration
* Patients with GBM/AA must not have received (i) nitrosoureas within 42 days of registration, (ii) any chemotherapy or experimental therapy within 28 days or 5 half-lives, whichever is longer, prior to registration
* Patients with GBM/AA must not have received prior anti-EGFR or EGFRvIII therapies (erlotinib, gefitinib, afatinib, osimertinib, ABT-414, ABBV-221, AMG-595, AMG-596 etc.)
* Patients with GBM/AA who have been treated with bevacizumab within the last four months are not eligible
* Received prior systemic biologic therapy (CAR-T, anti-PD-1 / anti-PD-L1, anti-CTLA-4, etc.) within 28 days prior to registration.
* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens including uncontrolled hypertension and active bleeding diatheses, which in the investigator's opinion makes it undesirable for the patient to participate in the trial or which would jeopardize compliance with the protocol. Screening for chronic conditions is not required
* Subjects who are human immunodeficiency virus (HIV), hepatitis virus B (HBV), and/or hepatitis virus C (HCV) positive
* Uncontrolled inter-current illness including, but not limited to:

* Symptomatic CNS complications that require urgent neurosurgical or medical (e.g. mannitol) intervention
* Seizures requiring a change in anti-epileptic medications (addition of new anti-epileptic or increase in dose) =\< 2 weeks of registration
* Known intracranial hemorrhage which is unrelated to tumor
* Significant medical or psychiatric illness that would interfere with compliance and ability to tolerate treatment as outlined in the protocol
* Illness/social situations that would limit compliance with study requirements
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* Patients with a "currently active" second malignancy other than non-melanoma skin cancers and carcinoma-in-situ of the cervix. Patients are not considered to have a "currently active" malignancy if they have completed therapy and are free of disease for more than three years prior to registration
* Any of the following cardiac criteria:

* A marked baseline prolongation of QT/corrected QT (QTc) interval
* (e.g., repeated demonstration of a QTc interval \> 480 milliseconds (ms) (Common Terminology Criteria for Adverse Events \[CTCAE\] grade 1) using Fridericia's QT correction formula
* A history of additional risk factors for torsade de pointes (TdP) (e.g., heart failure, hypokalemia, family history of long QT syndrome)
* The use of concomitant medications that prolong the QT/QTc interval
* Patients confirmed to have a cis double mutation (Del19/T790M or L858R/T790M) or cis triple mutation (Del19/T790m/C797S or L858R/T790M/C797S)
* Past medical history of interstitial lung disease, drug-induced interstitial lung disease, radiation pneumonitis which required steroid treatment, or any evidence of clinically active interstitial lung disease. History of hypersensitivity to active or inactive excipients of WSD0922-FU or drugs with a similar chemical structure or class to WSD0922-FU
* Refractory nausea and vomiting if not controlled by supportive therapy, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection that would preclude adequate absorption of WSD0922-FU
* Inadequate bone marrow reserve or organ function
* Patients with NSCLC LM who are unable to undergo collection of CSF
* Patients who are unable to tolerate dairy (GBM/AA cohort only). This is to ensure that patients on this cohort can participate in the food effect study

Note: Other protocol defined Inclusion/Exclusion Criteria may apply.

Eligibility last updated 4/22/2024. Questions regarding updates should be directed to the study team contact.