After Buck, the Bundy family dog, died, Lucky comes to the Bundy's and takes the place of his predecessor. Buck is in the form of a Spaniel, having been born again; he is being punished by God because of his enormous aggression towards cats. The dubbed voice of the dog remains unchanged, in order to illustrate this reincarnation. Al and his family does not notice that Lucky is the reincarnation of their first dog. In particular, Kelly and Bud love their four-legged friend, although they often have difficulties in handling the animal. In a relay, it turns out that Lucky will hump anything.
It is also implied that Lucky is gay as in the episode Lez Be Friends, he snubs Elaine's female dog, Frisky while on a doggy date set up by Elaine and Bud in order to cure Lucky's depression and comes home with a male bulldog wearing leather biker clothing at the end of the episode, where they head upstairs (Bud even suggests for Lucky to pretend that Frisky is Lassie while on the doggy date).