@Riot what actually happens if Jax gets a real weapon?

stays broken

Jax was very broken when he came out. So Riot removed him so they can fix him, and after some time they re-added him to the game. Which is the reason he sais "Suprise! I'm back". Because he was too "powerful", the League officials decided to give him a lamp to fight, instead of an actual weapon.

I'm guessing he'd probably kill you before you got to see

If the lore is any indication, he'd become unbeatable and go on another winning spree which would continue on to break the current winning spree record which he himself set before the Institute limited his power and no other champ has ever been able to match to this day.