how big of tires could i get with a 3 inch lift on a 2007 f-150 with 20" inch wheels?

 

The wheels don't make a huge difference unless you go with a really wide tire on a narrow wheel. I think your stock tire size is 29-30". Gaining 3" of lift, I would assume would give you 2" on top more space and 4" overall more tire space. I'd guestimate just shy of 35s would work, say 33-34". You might get away with 35-36" but you're getting wide and will have to do some work on the back spacing and probably trim the body a hair to get them to turn fully.