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

I don't think I understand the question. Does it not unlock the door when you press Button 1?

What do you want to do with the LEDs? If you just want to fade one off and fade the other on you could do something like this instead of digitalWrite(led1, HIGH):

for (int i=0; i <= 255; i++){
      analogWrite(led1, i);
      analogWrite(led2, (255-i));
      delay(10);
}