Lier: or somebody who lies in wait, i.e. ambush: http://dictionary.reference.com/browse/Lier but I have never heard anybody use the word

No. A Lier is someone who is lying down. (very rare) A liar is someone who tells lies, i.e untruths

The word is "liar". "Lier" does not exist.

"Liar, liar, pants on fire! " is what children call each other if someone tells a lie.

Not the same. Have some ice cream. It will help you think more clearly! :P