When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.
8,000lbs is fairly hefty load for any 1/2 ton truck, much less one that has to turn substantially larger tires than normal.
The 5.0L is a strong engine, I don't tow often with my FX4 5.0L, but I did recently tow 7,000lbs threw the mountains in new mexico and it handled the load very well, even at 8,000 feet above sea level it didn't feel overworked. For the record, my truck isn't lifted nor does it have larger tires on it.
So your engine has mustard to butter the sandwich no doubt. But I don't think it would it hurt anything to swap out your rear end if you are planning on towing 4 ton's with a lifted truck. 4.10's would do you good. 4.30's even better.
I say all this under the assumption that gas mileage is the least of your concerns.
I'd go 4.30s with 35s and 4.56s if you want to run 37s. It takes a lot of lift to run 37s on an F150 though, I would strongly advise against it if you tow.