Lie means "split." Although theorists often debate what precisely this means, the general consensus is that it refers to a division of energies in multiple directions at the same time. One model is in Fair Lady Weaves Shuttles, where the energy threads upwards, forward and to the side, causing the energy to "split" three ways to uproot and off-balance the opponent.
Lie in the steps is sometimes difficult to perceive. It usually exists in multiples of two directions: forward and to the side; backward and to the side; sideways (Wave Hands); forward and curving to the side (as in the turning steps). This last one can be seen in three directions if the step turns and shifts to a forward stance. The back leg pushes the opponent's leg one way while the front leg catches his other leg, lifts it slightly, carries it across your front (coiling), then pushes it along the line of your step. This is easiest in a 90- to 180-degree turn.
The same split can occur in an outward turn. As you turn to the outside, your leg contacts the inner thigh of the opponent's leg (right against right). Then you step in an arch (with the turn) and shift forward. This will carry his leg sideways and forward (fom his perspective, backward and to the side). This is dangerous, however, as it will require you to turn your back on your opponent for a moment. It must be done quickly and with strict observance of the position of his hands.