This trial is studying how well talimogene laherparepvec and pembrolizumab work in treating patients with stage III-IV melanoma. Biological therapies use substances made from living organisms that may stimulate or suppress the immune system in different ways and stop tumor cells from growing. Immunotherapy with monoclonal antibodies may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving talimogene laherparepvec and pembrolizumab may work better in treating patients with melanoma by shrinking the tumor.