The transmission valvebody and plastic cooling hoses.
The LR3 has a pretty ubiquitous trans, but they can have issues. Some in the know pick these up cheap and gamble that a failed VB hasn't caused more issues internally.
I guess it's a less common issue than the chain system on a 5.0, but it can be just as expensive to remedy or more. That was one big reason I went with the LR4 over the 3. Every part of the 4 is just noticeably better than a 3 in my opinion (interior, exterior, performance, etc.). The 3 has less big repairs in its pocket though, and if money is a factor they're cheaper. I'd take a high mileage 3 over a 4 if my budget didn't fit low mileage trucks (mid teens for 3s, low 20s for 4s). I have nothing against the LR3, I owned 3 before my first LR4, one of which had the HD package. The HD was an easy sand dune climber and nicer than its contemporary competitors. The 4.4 was just...adequate...though. It kind of felt like a stock 4.6 D2, and the power to weight ratio is similar. The way the 5.0 punches hard everywhere makes the LR4 actually fun to drive. The brakes are right there all the time and the suspension handles the weight incredibly well. I have always said I'd never consider a V6 LR4 because you could have a V8, but lower mileage V8s are older and harder to find. I imagine a V6 LR4 would be more fun than a LR3, but they're newer and more expensive.
The 4 does everything better when they're both working. The 3 is just more likely to be limping along.