Is there any trap I can build that will somehow force mobs into it and kill them? If it has to have lava is there a way to keep the items?
Yes, and yes. It's called a lava blade. Lava source 4 blocks into the wall with a sign holding up the last edge of the lava. Have a water stream running to this. The mobs float in it, but drop items from their feet where you can have a water stream to carry it to a collection point.