Lie (to fib): lie, lied, lied. (You lie, you lied, you have lied.)
Lay (to set down): lay, laid, laid. (I lay the book down, I laid it down, I had laid it down.)
Lie (to recline): lie, lay, lain. (I lie on the bed, I lay on the bed, I had lain on the bed.)
The first (to lie) is a simple verb. The second (to set down) is a transitive verb, meaning it conveys an action from the subject to a direct object. The final one (to recline) is another simple verb. Let's see if any other website makes as brief an explanation as this one.