Key Inclusion Criteria:  EBV+ relapsed/refractory lymphoma following 2 or more prior systemic therapies EBV+ DLBCL, NOS: Must have received at least one course of an anti-CD20 immunotherapy, and at least one course of anthracycline-based chemotherapy PTLD: Must have received immunotherapy with an anti-CD20 agent. Hodgkin lymphoma: Must have received at least one course of anthracycline-based chemotherapy. Patients with classical Hodgkin lymphoma should have failed or be ineligible for an anti-PD-1 agent and CD30-directed therapy. For extranodal NK/T-cell lymphoma patients only: Relapsed/refractory disease following 1 or more prior systemic therapies. Patients must have failed an asparaginase-containing regimen. No available therapies in the opinion of the Investigator Not eligible for high-dose chemotherapy with allogeneic/autologous stem cell transplantation or CAR-T therapy Measurable disease per Lugano 2007 ECOG performance status 0, 1, 2 Adequate bone marrow function  Key Exclusion Criteria:  Presence or history of CNS involvement by lymphoma Systemic anticancer therapy or CAR-T within 21 days Antibody (anticancer) agents within 28 days Less than 60 days from prior autologous hematopoietic stem cell or solid organ transplant Less than 90 days from prior allogeneic transplant. Daily corticosteroids (≥20 mg of prednisone or equivalent) within week prior to Cycle 1 Day 1 Inability to take oral medication, malabsorption syndrome or any other gastrointestinal condition (nausea, diarrhea, vomiting) that may impact the absorption of nanatinostat and valganciclovir. Active infection requiring systemic therapy (excluding viral upper respiratory tract infections).