Since getting my LR4 in 2010, I have probably put in something like 6 batteries, including the larger truck batteries (recommended!) I also use the TRAXIDE dual system to help out (also highly recommended!) However, these trucks are simply power hungry. I am putting in a new alternator with my engine rebuild (I am on the original and am sure it has seen better days) so that is always a consideration, but the reality is that these vehicles have a lot of ECU's and need a lot of juice. One thing I learned (the hard way) was to buy a digital battery maintainer and use it in the garage (obviously impossible if you are parked in the street). Especially important to hook that thing up before beginning any work on the vehicle. I probably killed my first two batteries tinkering with the truck thinking "Oh, I will just do this little thing" and then two hours later...still working. And the computer cannot go into sleep mode / low power when you are opening and closing doors and whatnot.
Hope that helps and the gang has a lot of great suggestions for bigger / better batteries.