those three verbs are not spelled the same, they do not sound the same, they do not mean the same, but they are irregular. you need to memorize them. my grammar ain't what it used to be, but this is right I think:
the following has the present tense, past tense, and past participle:
to lie(tell a lie)=lie, lied, lied.
to lie(down)=lie, lay, lain
to lay=lay, laid, laid
study the meanings in a dictionary.
