I did a fair amount of searching on the forums for information on whether or not 37" tires would fit on a 05'+ truck with a leveling kit. I did not find many trucks. I did quite a bit of measuring on the truck and decided that they would fit. The goal was to gain more clearance under the axles, fill the wheel wells up, and still be able to tow a goose-neck trailer.
I picked the tires due to their less aggressive, and hopefully longer lasting tread. They are 37"x12.50"-18" Yokohama Geolander's mounted on my stock 18" wheels. My truck has 2 1/2" spacers on the front springs and a 1" taller block in the rear. They get within 1" of the rear part of the plastic wheel well, but do not rub anywhere but the standard rubbing on the control arms at full turn. I cycled the suspension and far as the stock Rancho shocks will go, with out the tires hitting. I will be adding some sort of stop to the knuckles to keep the tries from hitting the control arms at full turn.
After driving the truck a few weeks, I could not be more happy with the tires. The ride has improved due to taller sidewalls. They are dead silent till 80+mph, and still no vibrations at those or any speed. I have driven through mud about 2 feet deep, the tread clears out well, but mud is not their strong suit. 37"s are still pretty small for such a heavy/large truck. They do seem to handle icy/snowy conditions MUCH better then the stock tires.
Truck has a full tank and about 700~800lbs of machinery and tires in the bed, so it's sitting a little low in the rear in the photos.
If anyone else is running this lift/tire combo, I'd love to see photos of your trucks. Thanks!