• Participants must be able to understand and willing to sign a written informed consent document.

• Participant must have signed and dated an IRB/IEC approved written informed consent form in accordance with regulatory and institutional guidelines. This must be obtained before the performance of any protocol-related procedures that are not part of normal subject care.

• Participant must be willing and able to comply with scheduled visits, treatment schedule, laboratory tests, and other requirements of the study.

• Participants must be at least 18 years old on day of signing informed consent.

• Participants must have a Karnofsky Performance Status (KPS) ≥ 70

• Participants must have histologically confirmed R/R primary DLBCL CNS lymphoma (from brain biopsy, CSF or vitreous biopsy).

• Participants should have evidence of refractory or recurrent disease on MRI with measurable or evaluable enhancing disease.

• Participants must have recovered to ≤ grade 1 or pre-treatment baseline from clinically significant toxic effects of prior therapy; exception, participants with ≤ grade 2 neuropathy may be eligible.

• Participant with dexamethasone requirement of ≤ 8mg/day or bioequivalent with corticosteroid usage at a stable or decreasing dose 2 weeks prior to screening.

• Participants must be able to undergo MRI.

• Participants must demonstrate adequate as defined below (all screening labs should be performed within 14 days of treatment initiation):

‣ Hematology

• White Blood Count (WBC) ≥ 2 K/µL

∙ Platelet count ≥ 100 K/µL

∙ Absolute Neutrophil Count ≥ 1.5 K/µL

∙ Hemoglobin \> 9.0 g/dL or ≥ 5.6 mmol/L (Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks)

⁃ Biochemistry

• Serum creatinine ≤1.5 x institutional ULN OR Measured or calculated creatinine clearance ≥30 mL/min for participant with creatinine levels \>1.5 × institutional ULN (Creatinine clearance should be calculated per institutional standard)

∙ Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x ULN (≤5 × ULN for participants with liver metastases)

∙ Total bilirubin (TBILI) ≤ 1.5 x institutional ULN (except subjects with Gilbert Syndrome who must have a total bilirubin level of \< 3.0 x institutional ULN) OR Direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 × ULN)

• Women of childbearing potential (WOCBP) must have a negative serum pregnancy within 72 hours prior to registration.

• WOCBP who are sexually active must use highly effective methods of contraception during treatment and for 28 days after the last dose of paxalisib. For male subjects with a pregnant or non-pregnant WOCBP partner, contraception measures are required during treatment and for 28 days after the last dose of paxalisib.

⁃ The subject, in consultation with the investigator, will select the most appropriate method of contraception from the permitted list of contraception methods, and site personnel will instruct the subject in its consistent and correct use as needed.

⁃ In addition, the investigator will instruct the subject to notify the site immediately if pregnancy of the subject or their partner is known or suspected.

⁃ Highly effective methods of contraception are those that, alone or in combination, result in a failure rate of less than 1% per year when used consistently and correctly and include:

• Established use of oral, injected, or implanted hormonal methods of contraception

• Correctly placed intrauterine device (IUD) or intrauterine system (IUS)

• Male condom or female condom used WITH a spermicide (i.e., foam, gel, film, cream)

• Male sterilization with appropriately confirmed absence of sperm in the post-vasectomy ejaculate

• Bilateral tubal ligation or bilateral salpingectomy