Judy, when Layla walks underwater, she is doing what is called spinal walking. This movement isn't controlled by the brain, but the muscles in charge of reflex remembering that when the front legs move in a walking motion, they used to move in a walking motion too, so it's a jerky kind of motion based on muscle memory. It's basically reflexive walking. She doesn't have the strength yet to hold her weight long while moving on ground, but the water is great because she stays afloat with her life jacket and they can work on just the movements of her legs instead of also holding her weight. I'm sure that eventually she can do it out of water too
Here is a video of another dog named Cricket, who is a yorkie cross owned by a lady I met on another forum for handicapped pets. She was told Cricket would never walk again, but he now spinal walks, and does very well at it!