I am replacing my alternator just now in my 2013 after it failed to due an oil leak on the right side of the engine. I am assuming it's the valve cover gasket, though maybe I didn't torque the oil filter housing correctly.
Also, remember that these are smart alternators and will not always be outputting the same voltage. I had a huge surprise on my 2016 LR4 on a trip in the Mojave last April when my USB/Voltmeter indicated only 12V output. Well, it turns out that my battery was so topped off from being on so much throughout the previous couple days, that the alternator just stopped charging the battery. Once I drained my battery a tad bit with engine off or whatever, the alternator ramped up it's outut.
Having said ALL that, haha, on my '06 LR3, I have the Traxide dual-battery kit (also on my 2016 LR4 but modified for use with a LiFePo battery). When I had lights, music, air-conditioning on all at the same time, I was getting pulsing headlights, etc. So I started researching higher-output rated alternators and found the Power Bastards 250A alternator. Now I won't use 250A (and I don't plan to rewire to be able to accommodate 250A flowing around), but the MAIN feature of this high output alternator is that at idle speed it is producing 125A and at only 1200 RPM it can push 250A. Basically, my LR3 no longer has power source issues. None at all. The batteries are always topped of and my lights never flicker with everything going. The stock alternator is great for a stock rig, but for my built out LR3 with dual-batts and all that jazz, being able to push 125A at idle is a game changer. In theory, the stock 150A alternator will ramp up output when demand is high, even at idle by adjusting the engine idle speed, but it's hitting it's full capacity. Anyway, my rig probably still only never demands more than 150A, but now my capacity is such that my alternator doesn't sweat any additional loads and I never have battery or electrical gremlins from low SOC batteries like before.
Oh, and a last note, there is a BMS reset function in the GAP tool when installing a new battery. I know this is for sure the case in the 2014-2016 LR4's but I haven't come across this function yet on the 2013 since I haven't changed that battery yet.