Depends on how much weight, TV and trailer. As a datapoint, my ~6500lb rig did fine towing 8k on 33.2" tall tires and stock gearing. Credit to the 5.7Ls strength. Actually, it got its best cruising MPG in this config as S4 was almost an S4.5 gear that was great for efficiency (10-11mpg). In the extreme grades and elevation of the Sierras and Rockies, it wanted more gear. Both for acceleration from a stop, falling into a torque hole in second gear and not being able to accelerate, and probably the biggest difference was engine braking. If you're trailer is any less than say 6.5k, and you watch the weight added to the TV, I think it'll work fine with a 33.7" tire.
Now that I'm on 35s with 4.3s, almost exactly stock gearing, it's definitely a solid improvement in the higher elevation mountains where I do a lot of camping. No more acceleration hole in second gear. And much stronger engine braking in 2nd gear where I can control momentum without physical brakes. It gets your attention when you can't keep downhill speed in check in even 2nd gear because physical brakes only go so far until they overheat. Then there's the grades where you know you're really heavy when needing to be in 1st gear to manage a section. I would re-gear for the safety of engine braking alone if really heavy.
I drive manuals and maybe that translates to the LX as I'm always in S4 and don't let it hunt (builds heat in the transmission when towing). Still enough torque with this gearing setup to manage mild hills. 3-5% grades, slap it into S3. 6%+, 2nd gear.