Have you done a cam swap in the LS2?
This is not apples to apples but annecdotal. I have a 2008 GMC Sierra Regular Cab/Short Bed that I bought new. It's a 2wd with a 5.3 and it had a 4L65E or 4L70E (not certain). I've done some typical bolts-ons including long tube headers, a cam, went to 4.10 rear gears (keep in mind, my 275-55-20 tires are nearly 32" tall), etc.
It's my daily driver and I enjoy driving it in a spirited manner. I did the cam swap at 82k miles. At about 114k miles 3rd started to go. I limped/babied it to 121k miles and then pulled it and had a performance build on it done (sun shell, shift kit, stacked pack on the 3-4 with an extra clutch, Corvette servo, etc., etc.). To be fair, the guy that built it for me may not have been the right guy for a performance build. The 1-2 shift was a bit aggressive (I liked it - would chirp the tires but he probably had one too many spacers in the 1-2 accumulator) and he probably should have advised me to put in a Billet Input shaft/drum and a billet output shaft along with the rest of the performance goodies. The first build didn't last but maybe 10k miles and it was pulling the input shaft out of the drum (re-used original). He mostly made good on it and installed the $900 billet input shaft/drum I supplied. That build lasted maybe 35k miles and the output shaft shattered on a wide open throttle 1-2 upshift. This was with a 5.3 with a mild cam (219/228 110LSA 525/525 lift).
At that point I felt like I was wasting good money after bad and I bought a 4L85E out of an 09 GMC Express 3500 cut-away van. I had it rebuilt and put a shift kit and some other performance goodies in it. At the same time, thanks to the advice of a friend on here, I did a lot better job matching the stall speed of the torque converter to my setup. With the 65E I was running a re-stalled stock converter (Circle D 278mm) 3200 RPM stall. With the 85E I'm running a 3600-3700 rpm stall. At first it was a little bit to get used to but what a difference! The truck is "fast" (It's still a 5000 lb. truck) and fun. The 278mm converter was too tight for the setup and the truck was a bit doggy on the low end. Either way you go, you need to plan on spending the money on a good converter that is well matched to your setup or you will be disappointed.
I've driven the 85E hard for 15,000 miles now. I did a drain and refill on it at 5000k miles and I'm about to do another, now that it's 10k miles later. That 4L85E is a beast. It takes anything I throw at it. It's the best thing I ever did to the truck. They shouldn't be putting 4L60/65/70E's behind anything making more than about 300 ft. lbs. of torque in my view and should have never put those transmissions in trucks.
If you are going to keep the LS2 totally stock and you aren't going to beat on it, in my opinion, you can get by with rebuilding the 65E but I would put the typical upgrades in it for durability while you are in there. Anything more than that and I strongly recommend the 80/85E. You won't regret it.
When I put the 85E in my truck I was worried about the different gear spread (taller first and less overdrive ratio). I overcame the taller first gear with more stall speed and a looser converter (I went with a 258mm Circle D instead of the slightly tighter 265mm unit they initially suggested). The truck performs better now that it ever did, speaking from a seat of the pants perspective. I've never taken it to a track. The steeper overdrive gear (numerically lower) isn't really that noticeable. With 4.10's and 32" tires, I turn around 2700 RPM at 85 mph. That gets a little old on a long trip because of the loud exhaust on the truck but it's not really that many RPM for the speed. Some perspective, it turns a little under 2000 RPM at 60.
With your 3.42 and the 2.48 1st gear ratio of the 4L80E, that gives you a final drive ratio in 1st gear of 3.42x2.48=8.48. I usually like to be in the 9's but I don't think this is terrible, especially considering the relatively short tire height (25.43") you have. My truck has 4.10x2.48=10.16 but has 31.9" tires. I think you can take care of any 1st gear too steep concern with torque converter selection. I think the LS2 makes enough torque that it doesn't need such a steep 1st gear as the 4L60/65/70E's 3.06:1.
Your 25.43" tall tire with a 3.42 and the 0.75 overdrive of the 4L80E should translate to about 2000 RPM at 60 and about 2900 RPM at 85. If the exhaust isn't too loud and the rest of the drivetrain and wheels/hubs/tires are smooth, this won't bother you, even on long trips. Here are a few calculators I really like...
Tire height calculator....
Tire Height Calculator by Wallace Racing
wallaceracing.com
RPM calculator - use the bottom section labeled "Transmission Final Gear Ratio Manual Entry" (torque converter locks)
I hope this helps.