The auto trans can make the process a bit fussier at times. For getting into low range, the gear selector needs to be in neutral and the vehicle stopped. High range is meant to be selected on the fly, but not while the rear wheels are slipping/spinning. That's not to say that it can't also be selected while completely stopped with trans in neutral in the same manner as low range. Coming out of low with the auto is often a two-handed approach. By that I mean, one hand will slowly cycle the gear selector back and forth between r-n-d positions while the other hand applies rearward pressure to the t-case lever. Once you get the lever out of low position and into neutral, if you encounter resistance going into 2h from neutral with the engine running, try shutting off the engine and waiting a beat. You should then be easily able to slip into 2hi and then re-fire your engine. These suggestions are intended for a single lever t-case. I don't know how much if any would apply to your twin stick setup.
T-case lube should only be sae 90 gl-1 mineral lube aka tractor lube, or straight 50wt racing motor oil. Nothing else.