Lift kits?

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.

Depends on how much lift and the type. A body lift would clear bigger tires but not mess with the suspension. A suspension lift depends too. Something like longer leaf shackles wouldn't change how the leaf carries a load although it might require longer bump stops. New springs obviously it would depend on the spring. Up front would likely involve new upper control arms and adjusting the torsion bars. I'm not really familiar with lifting GM trucks specifically so I'm just speaking in general terms. I do know they have leafs in the rear and a torsion sprung IFS. Another consideration is that lifted trucks generally don't play nice with fifth wheels.

Got a little long winded there but the short version is that you can tow with a lifted truck if you're careful about how you go about it and aren't planning on a fifth wheel.

Leveling keys and some good 33-34" tires, whatever you can fit under it without a suspension lift would be the best compromise, IMO.
A new HD pickup will tow 8klbs no problem though with any off the shelf 4-6" lift kit and 35s and still feel more stable than a stock 1/2 ton.
I prefer a spring lift in back instead of blocks, but with a gasser, traction control and all that, I wouldn't worry as much about the torque and axle wrap of blocks in back compared to something older with no tq mgmt and gobs of diesel power.
Your fuel mileage and power will be su ckyer with big tires and lift, but the drivetrain is robust to handle it now and for years to come.

But yeah, it's mostly for show since it will still have the turning radius of a school bus.
That said, lifted Chevies look cool!

Friends don't let friends install body lifts!

6.0 gas engine in a 2500 truck likely has only a 3.73 axle ratio.

If you go too much bigger with the tires, you'll be doing an axle gear change to make up for lost power with the bigger tires, to the tune of about $750 per axle.

Lift kits that use rear blocks can also increase axle wrap. I know Ford and Dodge use them without issues, but there is a reason Chevy doesn't use them. I am not bashing the others, but saying maybe Chevy doesn't use them for a reason. A 2015 Chevy 2500 sits pretty high as it is and raising it could cause clearance issues with a fiver.