I've had great luck with capturing too. It can take some time before you add the command and he's associating it with the action, but I guarantee that if you start marking (verbally - "yes!" or with a clicker) and tossing him a treat every time he lays down on the floor he will start doing it more and more frequently.
Using a clicker is the best way to do it. And don't treat from your hand, which raises his head, which may raise the body. The treat should be put on the floor between the paws.
With regard to luring, DON'T start at the nose any more. Get something that smells amazing (hot dogs, dehydrating lamb lung, smelly cheese, dehydrated tripe), when your dog is in a sit, put the treat between your pup's front paws, under his neck. If he tries to go for it by bending his neck (many will), push it a little further under her chest.
Some dogs move forward into a down. But a lot BACK into a down (especially when they're puppies). It's more comfortable (just like some dogs will naturally spin or roll over one direction or anyone). So if you're trying to get your dog to come forward to a down and she's a backer-upper, it won't be natural to her.
I was at the vet's office and a woman had a lovely hunting spaniel with her, about 6 months old. I asked if I could give the dog a treat. She said sure. I asked the dog for a sit. Dog sat. I asked the dog to lie down. The woman said "this dog won't lie down on command. I've tried everything."
I tried the technique I just outlined. It took a few tries. The dog kept backing up on me, so I moved my hand further under her chest; she mouthed my hand, but I held tight to my treat. Suddenly, she plopped down. Then, in rapid succession, she kept plopping down. After about 8 times, I started to put the word "down" to it. She Could down!! She just needed the right approach for her body/brain.