i get it now! necker cube! if it is an automatic door and she allows it to activate, that makes perfect sense to me in the english i am familiar with. of course, as you mentioned aaronyoung7, it might well be a standard expression in british, canadian, new zealand, or australian english (or pockets of the us that i am not familiar with).
I put "She leaves the door open" intending the meaning She allows the door to remain open" and although this was accepted, it does not seem to be what the given answer (lets) intends. I'm guessing ligeann covers both senses. The ambiguity in English lies in the word leaves, which could imply "allows to remain" or could simply indicate "permits to". or even "releases and thus enables the door to open" British English would normally have lets for the "release, let go, allow to activate" sense and leaves* for the "allows to remain in a state" sense.