Lie angle is, and I quote:

"The angle in degrees between the center line of the hosel and the sole of the clubhead, when the sole is touching the ground at the center of the face scoring area" (Practical Clubfitting Program).

It's a reference to how upright or flat your club sits at address. If they're toe down, you say your lie is flat. If they're toe up, you say they're upright.