This single-arm, open-label pilot study will assess the safety and efficacy of RN1701, a bispecific CD19/CD20-targeted allogeneic CAR-T-cell product, in patients with relapsed or refractory B-cell lymphoma. Up to 19 participants will be enrolled in a conventional 3 + 3 dose-escalation scheme. The primary objective of the study is to evaluate the safety and feasibility of RN1701 for the treatment of relapsed/refractory B-cell lymphoma. The secondary objective is to evaluate the efficacy of RN1701 for the treatment of relapsed/refractory B-cell lymphoma. The exploratory objective is to evaluate the expansion, persistence, and ability of RN1701 to deplete CD19- and/or CD20-positive cells in patients with relapsed/refractory B-cell lymphoma.