Is your lucid-dream self really yourself?

This is such a reductionist way of looking at the question. Obviously the dream world is made from your mind and only your mind. However, that doesn’t entail that who you believe to be yourself in a dream is the same person you believe to be yourself IRL. Your ‘mind’ isn’t necessarily synonymous with ‘you’. ‘You’ is created from different parts of your brain/mind working together. As other posters have said, the power your subconscious has is greater in dreams.