(The same is true, by the way, of sit.) In written material, we generally use down with lie when we mean to recline not because down is needed grammatically but because we wish to distinguish from the regular verb lie, meaning to tell an untruth (as in lie, lied, lied). If you tell your dog, Lie, as in (You) lie (down), that's a complete sentence. More on lie: In its simplest (command) form, when the you is implied, lie is a sentence all by itself.