Prephase Treatment With Prednisone +/- Vitamin D Supplementation Followed by Immunochemotherapy

Inclusion criteria 1. Histologically documented diagnosis of Diffuse Large B-cell Lymphoma or Follicular grade IIIb lymphoma, as defined in the 2017 edition of the World Health Organization (WHO) classification. 2. Age ≥ 65 years 3. Comprehensive Geriatric Assessment performed at baseline, before start of any treatment. 4. Eastern Cooperative Oncology Group performance status (PS) ≤3 5. Eligibility for anthracycline containing regimen (R-CHOP or R-miniCHOP) 6. No previous treatment for DLBCL or Follicular grade IIIb lymphoma 7. Ann Arbor stage I-IV 8. At least one site of measurable nodal disease at baseline ≥ 1.5 cm in the longest transverse diameter as determined by CT scan ; or one metabolic active site of disease at baseline FDG-PET scan 9. Serum basic levels of Vitamin D \[25 (OH) VitD\] ≤ 40 ng / ml; 10. Adequate hematological counts defined as follows: * Absolute Neutrophil count \> 1.5 x 109/L unless due to bone marrow involvement by lymphoma * Platelet count ≥ 80.000/mm3 unless due to bone marrow involvement by lymphoma 11. Adequate renal function defined as follows: \- Creatinine ≤ 2 mg/dL, unless secondary to lymphoma 12. Adequate hepatic function defined as follows: \- Bilirubin ≤ 2 mg/dL unless secondary to lymphoma 13. LVEF \> 50% at bidimensionally echocardiogram 14. Life expectancy ≥ 6 months 15. Subject understands and voluntarily signs an informed consent form approved by an Independent Ethics Committee , prior to the initiation of any screening or study-specific procedures 16. Subject must be able to adhere to the study visit schedule and other protocol requirements 17. Men must agree to use one of the below reported acceptable method of contraception for the duration of the study and for 3 months after receiving the last dose of immunochemotherapy, and to not donate sperm while on study. Exclusion criteria 1. Histological diagnosis different from Diffuse large B-Cell Lymphoma or Follicular grade IIIb lymphoma, including diagnosis of HGBL, with rearrangement of MYC, BCL2 and/or BCL6 (double-hit) 2. Use of VitD supplementation as standard of care at dose higher than 10,000 U/week 3. Suspect or clinical evidence of CNS involvement by lymphoma 4. Contraindication to the use of rituximab 5. Contraindication to the use of VitD supplementation (Hypercalcemia/Hyperphosphatemia) 6. Subject has received any anti-cancer therapy including chemotherapy, immunotherapy, radiotherapy, investigational therapy, including targeted small molecule agents within 14 days prior to the first dose of study drug 7. Significant history of neurologic, psychiatric, endocrinological, metabolic, immunologic, or hepatic disease that would preclude participation in the study or compromise ability to give informed consent 8. Any history of other active malignancies within 2 years prior to study entry, with the exception of adequately treated in situ carcinoma of the cervix uterine, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin or limited stage surgically removed breast cancer or adequately treated with radiation therapy or limited stage prostate carcinoma surgically removed or adequately treated with radiation therapy or previous malignancy confined and surgically resected with curative intent 9. Evidence of other clinically significant uncontrolled condition including, but not limited to: * Uncontrolled and/or active systemic infection (viral, bacterial or fungal) * Chronic hepatitis B virus or hepatitis C requiring treatment.