4x4 trail or road? Two different trails, one on each side of the lake. That will vary the answers greatly
If it's HITR Road, I would say yes, he should be able to without much problem. If it's HITR 4x4 Trail, then I will say it depends. Could a good driver make it in that setup, sure. I saw rholbrook's 16-17 year old kid (at the time) drive it in a stockish LJ on slightly larger tires with no rear locker. So it's doable, but there are a few sections that could get sketchy, especially for a driver that's of unknown capability.
x2.
I say "no". A "leveling kit" isn't the same as a lift. I'm guessing most people with a leveling kit and bigger tires haven't fully flexed out their rig to see what rubs and where it rubs. I wouldn't want to be leading the trail with someone in the group driving a tahoe (unless it was Bart, who could drive an 18-wheeler up there). I would recommend he take a 4x4 quad instead, that could be a lot of fun.
The trail isn't the most hardcore in the world, but there are some spots that could prove fatal or near impossible to recover from if a mistake is made. I would not be the least bit surprised to hear of frequent rollovers on the trail with inexperienced wheelers. We had to tow a rig out of there for about 10 miles last year, over obstacles and climbs. At one point we had to hook up a tow vehicle in front of the tow vehicle for traction. It's EXTREMELY remote out there, and there isn't cell coverage for most of the trail. Even if you managed to get off the trail to the trailhead, you're still a good 2+ hours from any real town. It'd be like wheeling a trail in Moab, without the support/town of Moab and the nearest town being Green River or Price.
Last year we let a lady tag along with us who said she was "very experienced" off-roading and rock crawling. She wasn't, and her rig was plenty capable, but she put herself and others in danger with her lack of experience, and ultimately decided to turn back about 1/4 into the trail. She was very uncomfortable, and we hadn't even made it to any of the challenging sections yet. Her lack of self-control over her fear was extremely dangerous.
Here are two videos from the past two years to get you excited on the trip:
[video=youtube;F8sAn8dOwUU]http://www.youtube.com/watch?v=F8sAn8dOwUU[/video]
[video=youtube;zJxIaIIOKzw]http://www.youtube.com/watch?v=zJxIaIIOKzw[/video]