Are you sure you want to ask??? There are essentially 3 different verbs here, but will treat your 2 verbs first.
1) to lie (down) intransitive : has no object, so e.g., "I lie down on the bed"
lie (present) *** lay (past) *** lain (past participle)
2) to lay (down) transitive : has an object, so e.g., "I lay down the apple on the bed"
lay (present) *** laid (past) *** laid (past participle)
You can see that these two verbs differ in modality, and both are irregular (in conjugation). Also, there is some overlap between words, which causes the most difficulty in use. There is the further complication that some people will make a reflexive pronoun as the object, e.g., "I lay myself down on the bed".
3) to lie (i.e., not tell the truth) -- generally intransitive
lie (present) *** lied (past) *** lied (past participle)
This is a regularly conjugated verb, but you can see the overlap of the particular word in the present tense with (1) above. There are also some idiomatic use of one or more of the verbs above.