Inclusion Criteria:

Newly diagnosed aggressive lymphoma or CLL/small lymphocytic lymphoma (SLL) that meets disease specific criteria below:

• Study 1 - Aggressive lymphoma
  • Newly diagnosed de-novo DLBCL or primary mediastinal B-cell lymphoma that will be treated with an anthracycline-containing regimen (rituximab-cyclophosphamide, doxorubicin hydrochloride, prednisone [R-CHOP] or equivalent); patients with composite lymphomas can also be enrolled as long as they have large cell component and will be treated with an anthracycline; in addition, patients with "B cell lymphoma, unclassifiable, with features intermediate between diffuse large B cell lymphoma and Burkitt lymphoma" or post-transplant DLBCL are also eligible as long as they meet other criteria; patients with typical Burkitt lymphoma are not eligible
    • NOTE: patients can be enrolled up through day 1 of cycle 3 of therapy; the patient is permitted to participate in any other therapeutic therapy for their disease as long as it does not concern vitamin D; patients can begin their chemotherapy while awaiting vitamin D results and treatment arm assignment or
  • Newly diagnosed untreated peripheral T-cell non-Hodgkin lymphoma (NHL) that will be treated with chemotherapy; NOTE: patients can be enrolled up through day 1 of cycle 3 of therapy; this includes the following disease types:
    • Peripheral T cell lymphoma, unspecified
    • Anaplastic large cell lymphoma (T and null cell type)
    • Extranodal NK/T-cell lymphoma, nasal type
    • Enteropathy-type T-cell lymphoma
    • Hepatosplenic T-cell lymphoma
    • Subcutaneous panniculitis-like T-cell lymphoma
    • Angioimmunoblastic T-cell lymphoma
    • Anaplastic large cell lymphoma - primary cutaneous type and
  • Willing to provide tissue for correlative research purposes
• Study 2 - CLL/SLL
  • Newly diagnosed (< 12 months from pre-registration on this study) CLL according to the National Cancer Institute (NCI) criteria or SLL according to the World Health Organization (WHO) criteria; this includes previous documentation of:
    • Biopsy-proven small lymphocytic lymphoma
    • Diagnosis of CLL according to NCI working group criteria as evidenced by all of the following:
      • Peripheral blood lymphocyte count of > 5,000/mm^3; if present, prolymphocytes should be < 55%
      • Immunophenotyping consistent with CLL defined as:
        • The predominant population of lymphocytes share both B-cell antigens (cluster of differentiation [CD]19, CD20, or CD23) as well as CD5 in the absence of other pan-T-cell markers (CD3, CD2, etc.)
        • Dim surface immunoglobulin expression
        • Restricted surface kappa or lambda light chain expression
      • Before diagnosing CLL or SLL, mantle cell lymphoma must be excluded by demonstrating a negative fluorescent in situ hybridization (FISH) analysis for t(11;14) (immunoglobulin H [IgH]/cyclin D 1 [CCND1]) on peripheral blood or tissue biopsy or negative immunohistochemical stains for cyclin D1 on involved tissue biopsy
  • Rai stage 0 or 1
  • Previously untreated
  • Asymptomatic with the plan for observation
  • Life expectancy of at least 24 months
  • Willing to provide tissue for correlative research purposes
  • Willing to be randomized to placebo for one year
• Both Studies:
  • Capable of swallowing intact study medication capsules
  • Serum calcium < 11 mg/dL; note: patients with hypercalcemia can be enrolled after the calcium is corrected with standard of care treatments
  • Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study)
    • Note: During the Active Monitoring Phase of a study (i.e., active treatment and observation), participants must be willing to return to the consenting institution for follow-up
  • Willing to provide blood samples for correlative research purposes
  • Vitamin D level (25 hydroxy D2 + hydroxyl D3) confirmed by central laboratory review