It’s pretty well documented that the LR4 uses a very weak charging profile. The computer controlled alternator only charges infrequently, and rarely at its highest level of 14.2v, presumably to reduce drag (parasitic loss) and boost gas mileage. This is particularly true if you take frequent short trips like 10-15 minute errands, commute, etc. Unless you run the car at highway speeds over lengthy hour or longer trips the battery’s resting state of charge never goes above 65-70% (12.25-12.30v) instead of the normal 100% of 12.67v.
I had all the classic issues discussed here with my 2011 LR4. Then with a fresh battery and dealer confirmed “optimal” charging system, the IID live data tool graphed the charging profile over varied conditions for a few weeks. I tried different batteries and styles (AGM/Non), but all had the same result… resting state of around 12.25-12.30v. Others found the same results with the IID tool. It was actually comical and there are lengthy posts on other sites as we saw the erratic charging profile draining the fresh batteries down as we went about our day. It's a pretty sophisticated profile that senses hillls, brakes, speed, has a warm-up profile, etc., but, it’s normal. A charge of 65-70% appears to be the target.
Generally, it’s not cause for concern. While the low state of charge will eat a battery a bit earlier than normal, in every-day use you don't really notice it. Unfortunately the marginal charging is clearly a disappointment when you need a bit of reserve. For camping off grid, you’ll see regular posts about turning off interior lights, changing to LEDs, etc. since the battery drains down so quickly from its low state of charge. Its not uncommon from just occasional courtesy lights and car remaining "active" (by having the key nearby) to have it drain down to a no-start state overnight.
I like to camp off grid with a rooftop tent, kids opening/closing doors, etc. so installed the 2nd battery option with the Traxide kit to compensate. But, once again only saw a resting state around 12.32v on even the 2nd battery. The extra capacity of the 2nd battery was nice, but I was missing over 50 amp hours of reserve between the two batteries being kept low. Not to mention the likelihood that the batteries would have short lives.
The solution? Until someone like the IID guys find a way to change the charging profile a lot of the LR4 guys simply plug their batteries in to a charger once a month, particularly before they go to remote locations and dry camp. Kind of ridiculous with this level rig, so I put two small solar panels between the forward-most slats on my factory roof rack. They're tied in to the 2nd battery and provide a 40 watt boost that tops off the batteries nicely to 12.67v. After a few days the resting state measured first thing in the morning was consistently 12.67v.