Cholecalciferol in Improving Survival in Patients With Newly Diagnosed Cancer With Vitamin D Insufficiency

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 * 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 Exclusion Criteria: * Patients with Burkitt lymphoma or any patient receiving rituximab-cyclophosphamide, vincristine, doxorubicin, high-dose methotrexate / ifosfamide, etoposide, high-dose cytarabine (R- CODOXM/IVAC) * Patients who previously had indolent lymphoma and now at a separate episode have large cell NHL (i.e. transformation