I've often seen greyhounds running in their sleep and it is always funny. My last greyhound, Eris, who never barked would often have plenty to say while she was dreaming. Sometimes her barking would cause her to wake up.
Luna is no exception. She dreams a lot of running, but when she was on her pain medication the chase was even more intense. Watching her run in her sleep was very encouraging to us because it showed that the neurons in all four legs were still firing. At times she would be in a full sprint with her legs kicking hard. Sadly, we never got a video of this because every time we turned the camera on, she would stop.
The best moment happened when she was still on her medicine. After she had spent several minutes running in her sleep she returned to a peacefully rest for a few minutes. When she went back to dreaming, she was no longer chasing her prey. Only her face muscles and ears were twitching. From the looks of it, she had finally caught her prey and was giving it what for. Mike and I laughed as quietly as we could, but eventually she heard us and woke up. I have never seen a dog dream of chasing and catching something before . It always seemed to me that they were forever chasing.
It's nice to see that Luna sees herself as catching that elusive rabbit. You got to love her optimism.