What's the biggest...
 

Tire I could fit under my stock Lincoln Mark LT truck???

I was going to do a level but was looking at some 33.12.50.18 Toyo or Mickey Thompson and some XD wheels would I be able to make this work at stock height???

It's a 4x4

33s should fit depending on backspacing of the rim. If you level it, 35s will fit, again depending on backspacing.

04Lariat is dead on. If using stock wheels 295/65/18 may be a better choice. 12.5 inch wide 33s are a little much for 7.5 inch wide stock wheels. The 295s will be slightly thinner, but real close to same height.