• 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

• 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