Both words, Down or Lie, can be used because they are simple commands, but for obvious reasons only use one, or as an alternative but slightly less preferred, “Lie Down” is adequate but again only if used consistently.
Initially this can be done from the sitting position simply by gently pulling his front paws and lowering him to the ground then rewarding and praising, etc.
“Down” from a standing position can also be trained. From both the sitting position or when he is standing, each time he lies down naturally repeat the command and accompanying gesture. As with other basic commands it reinforces the message and praising quickly if possible as the behavior naturally occurs will further encourage your dog.
Bear in mind that he is likely to lie down after exercise, creating an opportunity for you to use the reinforcing “Down” as he does it naturally, so this situation is an exception to the normal training aspect of requiring your dog to be alert.
By using a favorite toy in front of him in the Sit position, by lowering it to the ground directly in front of him, possibly as close as his nose, this will also encourage him to lie down, again as you accompany it with the command and gesture. A food reward will obviously also work but is best used sparingly.
With the behavior of lying down in particular, because it is natural your dog may not realise initially why he is being praised, but after a while through repetition he will. Training him to roll over or a similar further action involving lying down will also make it more natural that he responds to the Lie command.
As part of the training of this command, if done in a timely and non-forcing manner, a gentle touch on your dog’s shoulders as he starts to lie down may prove useful.
As your dog starts getting used to the start of the Down, it is a good idea to make sure that he stays down until told that he can get up. Use of the Stay command is appropriate for non-exhibition training.