Where can I find the Vault-Tec lab coat?

The Cambridge polymer labs and vault 81 contains guaranteed lab coats.

Just be aware there are quests in both locations that you must start before you are able to access the area with the lab coats.

You can come to the settlement called "Covenant".

After your investigation there, you come to the "Covenant Compound". While clearing it you will find a lot of Vault-tec lab coats.

It is part of the mission "The Human Error".