Since Audrey II was so cumbersome, that meant the foam rubber lips couldn’t move fast enough to synch up with the audio during any of of the songs. This meant that the team needed to filming the puppets at a slower-than-average rate of 12 or 16 frames per second, then speed up the footage to the standard 24 frames per second. Frank Oz explains in many interviews that, "it was a bitch." So, whenever you see Rick Moranis (who played Seymour Krelborn) or one of the other actors singing side-by-side with the Audrey II, he/she is really lip-syncing in slow motion.
Fun Litttle Shop of Horrors nerdy fan facts, right?