@Deann216 Among the excellent points made above by @Katrina79 , one that stands out as particularly important is that (depending on your local rental laws) this guest may acquire the legal right of tenancy during a 2-month stay and become very difficult to get rid of. When this happens, there's nothing Airbnb can do to help. With this in mind, things are off to a very ominous start.
The guest may have a valid reason for requesting an additional lock, so it's worth hearing out this person's reasoning with an open mind. But there's a big difference between a "request" and a "demand." Guests do not have the right to demand that hosts add features that weren't advertised, and those who attempt to do so right at the beginning of the stay are almost certain to become toxic tenants. If you have any inkling that the guest is trying to back you into a corner here, it can't possibly be worth it to keep this booking.
A small demand like this usually turns out to be a little test to see how easy you are to manipulate, and this is not a test you want to fail. Just imagine how easily a complaint about the locks at the beginning of the stay can shift to a phony robbery claim and a full refund a month later - sadly, this kind of scam is rampant. Personally, I would ask the guest to leave immediately and refund the remainder of the stay the minute they became demanding. However, before taking such a drastic action I'd want to be sure that there wasn't a miscommunication.
A written record of your dialogue should be kept in the Airbnb messenger for reference, but I think you get a better assessment of the guest's character and intentions if you first have the discussion in person.