Why does the ceiling fan work but the lights on it will not turn on after a power outage?
Could be a number of things.
I've had ceiling fans that are on two different circuits: one for the fan, and one for the light. It could be that the breaker is thrown on one circuit but not on the other.
It could also be that a surge caused the outage, and that burned out the bulb, the switch inside the fan, the switch on the wall, or any add-ons such as wireless remotes.
It could be that the light is on a 3-way switch, and someone flipped the other switch in trying to get the lights to work during the outage.