I'm having the same trouble with my puppy. I tell her to sit first, then I lead her down with the treat (hold it on your hand and only open your hand once he's down), but she won't do it without the gesture, so we're working on that.
Using something he really loves to eat will help. Once he gets the laying down part, he may not do it without you leading him down with the treat. So what I'm doing is saying "down" and then I wait 1 second, then lead down with the treat. And the next time I wait two seconds and lead down with the treat, and so on. Eventually he will start laying down without you leading him down, cause he'll get what's next after you say "down". I hope that makes sense! It works, but you have to be patient. Sometimes I have to wait 20 seconds before my dog will lay down, but I always make sure to just say "down" once, or the word loses meaning.
Good luck!!