Servo as a door lock, How can I ignore a button until later in the program?

I don't understand what your question is. The only problem with your sketch that I see is the use of delay. This way you might loose a opening signal if your waiting for the door being locked. Try to eliminate these by storing the time of an event and checking that against millis().

I don't know why you wanna display a boolean information (locked/unlocked) using PWM (which is kind of analog output). What's your intention there?