The Fallout wiki lists this apparel item as being in the dockhouse south of the Harbormaster hotel. I think I found the place (with a dead brahmin outside) but its suitcase contains a Postman Uniform. Where can I find this +2 INT coat?
Edit: I also checked Vault 111 again and you cannot loot the skeletons or overseer—they just have an "Activate" function and your character says that everyone is dead. I didn't see the lab coat anywhere else there.