Inclusion Criteria:  Primary or secondary CNSL (PCNSL or SCNSL) confirmed by histology or cytology. Renal insufficiency defined as a glomerular filtration rate (GFR, assessed by CKD-EPI or MDRD equation) of 40-80 mL/min or patients with a GFR >80mL/min who have experienced renal failure, defined as doubling of the serum creatinine compared to the baseline value during a previous HD-MTX treatment. Age ≥ 18 years (male or female). Life expectancy >3 months. Adequate organ function (i.e., bone marrow, liver, lungs) allowing intensive chemotherapy with MTX. Adequate clinical pathology values: Absolute neutrophil count ≥1.0 x 109/L, hemoglobin ≥9mg/dL (transfusion allowed), platelets ≥100 x 109/L. Total bilirubin ≤1.5x the upper limit of normal except for patients with known Gilbert syndrome. Alanine amino-transferase (ALT) and aspartate amino-transferase (AST) ≤2x the upper limit of normal. Alkaline phosphatase ≤2x the upper limit of normal. Prothrombin time within the normal range for the institution. Signed informed consent by the patient or legal representative prior to start of any study specific procedure. Females of childbearing potential and males must be willing and able to use an adequate method of contraception to avoid pregnancy for the duration of the study in such a manner that the risk of pregnancy is minimized. Acceptable contraceptives include intra-uterine devices (IUDs), hormonal contraceptives (oral, depot, patch or injectable) and double barrier methods such as condoms or diaphragms with spermicidal gel or foam.  Exclusion Criteria:  Ongoing or expected need for therapy with drugs interfering with MTX-clearance (i.e., beta-lactam antibiotics, NSAIDs, probenicid, salicylates, sulphonamides) or other nephrotoxic drugs. Prior brain radiotherapy within 28 days of first dose of the study drug. Concurrent illness interfering with hydration (i.e., relevant congestive heart failure, SIADH syndrome). Relevant third space (i.e., pleural effusion, ascites, extended edema) precluding HD-MTX treatment. Obesity (body mass index >30 kg/m2). Uncontrolled diabetes. Active hepatitis. HIV-infection. Pregnant or lactating woman. Participation in any other clinical trial either 1 month prior to or during this study. Previous intolerance to any of the drugs used in this study (i.e., MTX, LV)