I ran away from Tapu Lele, and I heard that you can only catch it again after beating the Elite Four, but I don't want to battle Professor Kukui again. Do I really have to fight him again?
1 Answer
As to whether you'll need to fight Professor Kukui specifically, you might:
Yes, you will need to beat the Pokemon League again in order to have another opportunity to catch Tapu Lele, as explained in this article:
If you KO the Tapu instead of catching it, you can get another chance by battling the Pokémon League again.
However, it's not guaranteed that you'll be fighting against Professor Kukui again. A full list of potential challengers is given in the answer to this question.
In your case, a good idea would be to try to catch the remaining Tapu Pokemon before re-challenging the Pokemon League, though, since if you fail to catch any of the others, they will all be respawned once you beat the Pokemon League again.