My experiences with lucid dreaming are not quite like that...
I recently did a project for a psychology class in which I kept a dream journal for three weeks, writing down every detail from every dream I could remember and then, the next night, telling myself that I would remember my dreams the next morning. I have always had good dream recollection and many lucid dreams, but this project helped me compile some statistics.
I have approximately 1.5 dreams a night. Once, during those three weeks, I had up to seven distinct dreams on a single night. Also, 24% of my dreams are lucid.
Unfortunately, when my dreams are lucid that doesn't mean that I can do whatever I want to do. I cannot control the actions of the people around me; only my own. And I can only control my environment itself to a certain extent. For example, I can launch my house into space or add snowmobiles to a mountain, but I can't just decide to abandon one dream in favor of an entirely different location. Also, there are varying degrees of lucidity. Sometimes I am aware that I am dreaming and yet cannot control anything; other times I can consciously control everything I do and yet am not really aware that I am dreaming at all.
I have not become my fursona in a lucid dream... it's never made sense to be a furry, before, in the context of them. I have, however, become an alien, or a superhero, or any number of things... (Unfortunately, the one thing I can NEVER do in my dreams is fly. Never had a flying dream; not once.) If I were to somehow transform into my fursona, however, I doubt the experience would be satisfying. My dreams never make sense and always have "what the heck" elements, if you will. If I want everything to be perfect, I'll just stick with my imagination...