hm what could work as an incentive, once you lot and obtain an item, you then enter a counter that allows you to increase your lottable amount by 1 for the next week but only if you fight all 4 bosses at least 4 times each.

Basically you enter dungeon, get a drop off Behemoth, then from that point on you have to kill/assist in defeating each boss 4 times to be granted an additional lot for the following week only to a max of +1.

Least this way it grants incentive for players to continue past lotting on the item of their choice and gives them a bit of reward for helping others out, allowing them the chance to obtain loot faster.