The Lincoln Lodge isn't really a place. It's a group that takes over the back of the Lincoln restaurant and puts on stand-up shows. And as far as I know they own all of their own equipment, and don't rent out space or time for sketch/improv groups.
They do have a "variety" slot at the end of their stand-up showcase, for which they bring in acts that aren't stand-up.
For info, you should toss them an email. I think their contact stuff is all on
www.thelincolnlodge.com.
I've performed in their variety slot a few times. They do a payout based on audience members for the night, but no split of the box. The actual stage space is veeeeery tiny, but the room is small enough that you can do without the mics if you have to.