Jersonija...
A few things to consider first...The LG G3 should have OTG USB support, so a simple plug-and-play is all you should need. You said that the MiniLab is not responding, but does that mean it's not powering up, or that it does and pressing any keys doesn't give you any sound? If it's situation 1, then either the phone really isn't OTG compliant, or the cable is an issue. The MiniLab itself shouldn't be a problem, but if you can test it on something else, like a PC or Mac running your DAW, then you'll know what's wrong for sure. If it's situation 2, you might need to check if Caustic and the MiniLab are talking to each other, or if the instrument you're using isn't muted. I take it you know that, if you're just starting a new song, that too will give you no sound.
By the way, I use Caustic on my Samsung tablet. If you're on the forum for Single Cell Software, you can ask there and see if you can get any help with this issue there as well. Hope that helps...
Side Note: Caustic...on a cell phone...? I've heard of stranger things before...
-oH-