This paper proposes a locality-sensitive hashing based multiobjective memetic algorithm namely LSH-MOMA for solving pickup and delivery problems with dynamic requests (DPDPs for short). Particularly, LSH-MOMA is designed to find the solution route of a DPDP by optimizing objectives namely workload and route length in an evolutionary manner. In each generation of LSH-MOMA, locality-sensitive hashing based rectification and local search are imposed to repair and refine the individual candidate routes. LSH-MOMA is evaluated on three simulated DPDPs of different scales and the experimental results demonstrate the efficiency of the method.