Personally I think 18" wheels and E rated tires are a minimum but then again I run Colorado trails. I have 18" LR3 wheels with 1.25"
MotorSport Tech spacers on my 2011 LR4.
The factory wiring to the 7 pin rear connector is very light weight. Say 16 gauge at best? A quick check with
BlueSea Circuit Wizard using 12V, 25' wire length (guess on how long the LR4 wire length is) and even just 10a load recommends at least 10awg. At 20a it is 8awg. You can play around with the calculator which will show that 16awg is good for ..... 3a. Yes it will charge the trailer battery but the voltage drop at load will result in a partially charged trailer battery.
My solution was to add a
BlueSea SI-ACR Automatic Charging Relay - 12/24V DC 120A in the engine bay,
fuse block and 8awg hot
and ground run to appropriately sized trailer connector. The ACR automatically combines batteries during charging, isolates batteries when discharging and when starting engines.