It's been proven that many animals do dream. But I highly doubt they can lucid dream. They are not sentient like you or I. The conscious sense of self that is required to lucid dream is probably not present in any animal. It's what makes us humans unique. Our prefrontal cortex is very active during a lucid dream, but not nearly as much during a normal dream. So we can infer this to mean that the prefrontal cortex is probably pretty essential to achieving consciousness within a dream. Non-human animals have very little, to no, prefrontal cortex and many evolutionists believe it is the part of the brain that ultimately sets us apart from non-sentient primates and all other animals. So with that all in mind, I'll again suggest that no, animals probably cannot lucid dream.