Not sure exactly what/how much rubbing with the -6 backspacing. Probably manageable, but... A spacer (assuming you mean wheel spacer?) will make it WORSE not better. The further out the wheel is the larger the arc it occupies so the outside edge of the wheel will hit the inner fender etc more.
The 5th gen tire fitment guide (see below) shows that with stock -13 offset it will posibly rub some, so at -6 it'll be a little more. The lift itself doesn't fix much rubbing, if you turn your tire that you have now till the outter edge is at it's closest point to rubbing something. Then imagine the body up 2-2.5 inches, you can see the clearance there doesn't change much if at all. The lift improves body contact above the tire but not so much in front or back. (Atleast between 0 and 2.5 inches)
http://www.toyota-4runner.org/5th-gen-t4rs/156378-5th-gen-tire-fitment-guide.html#post1550444