From what I understand, you only get the elemental damage bonus from arrows/bolts if the crossbow/bow shares the same elemental upgrade path. So a fire Avelyn is a waste. Go with lightning.
Also remember that every time you add a new damage type it has to go through the applicable defense. So even if fire worked with lightning bolts the physical would remain the same but the crossbow fire damage would go up against fire defense rather than double teaming the lightning defense with the bolts. That's assuming it did three damage types which it appears it would not.