Belial will not drop anything if you don’t open the boss lair chest.
I didn’t have any more materials to open the chest, but I stayed to help defeat some bosses. I noticed that if you defeat a boss lair and don’t open the chest, then if Belial appears and is defeated, he won’t drop any items whatsoever.
If player helps and defeats Belial, they should get the same drops that anyone else did regardless of they opened the boss lair chest or not.