I just got a newish 2015 Silverado 2500hd 6.0, long bed crew cab 4x4. My last truck was a toyota tundra 4x4. The tundra 5.7 easily pulled my 8,000 lb Arctic fox 25r but the handling was too squirrel...
It depends how the lift is done. Many lifts use soft spongy rear springs, which is definitely not good for load carrying or towing. If the lift uses springs at least equal to or better greater than the rate of the factory springs, it will be fine.