When you don't tell the truth, you lie. You also lie down when you're sleepy and wonder what lies ahead of you.
If we leave aside the lie that is an untruth, most meanings of lie are related. If something lies ahead of us, then it's there, down the road, waiting for us. If mountains lie to the east, we can think of them as having settled down there. If something lies unused, it is just sort of left to lie on the shelf (or wherever). If you let a sleeping dog lie, you're just letting him be right where he is — in the same position.