the first thing i think about is that joints which move eyelids are not connected to the main skeleton. What this guy said. If the eyelids have joints you need to parent them to an appropriate place on the fish's skeleton (a joint in the head somewhere, so the eyelids move with the head) and if not you need to parent the eyelids themselves to the skeleton. I can't remember which way around it is, but you either need to select the joint and then the eyelids and go to edit -> parent (or just press 'p'), or select the eyelids and then the joint and then parent.