This study will evaluate the preliminary safety, tolerability, and dose-limiting toxicities (DLTs) of Sym021, an anti-programmed cell death protein 1 (PD-1) monoclonal antibody (mAb) . The goal is to establish the maximum tolerated dose (MTD) and/or recommended Phase 2 dose (RP2D) of sequential escalating doses of Sym021 when administered once every 2 weeks (Q2W) by 30-minute intravenous (IV) infusion to patient cohorts with locally advanced/unresectable or metastatic solid tumor malignancies or lymphomas that are refractory to available therapy or for which no standard therapy is available. If an MTD is not identified, a maximum administered dose (MAD) will be determined.