ALF hypnotizes Lucky to make him think he is a bagel.
Lucky the Cat is the Tanner family pet in the ALF TV series. After Alf comes to live with the Tanner family, Lucky's existence becomes somewhat more precarious, since cats are a culinary delicacy on Melmac.
Once during a feeding frenzy, Alf is believed to have eaten Lucky, but he is later found. Alf ran off looking in the outside world, but is caught by a rescue shelter worker who doesn't know what kind of creature Alf is. Alf tricked the rescue shelter worker into releasing him so that he can grab the cat that looks like Lucky to bring home. Although it turns out the cat that Alf grabbed isn't Lucky, he still was not allowed to eat the cat he just took from the shelter. Alf actually tried to hypnotize the cat the same way he did to Lucky at the beginning of the episode (Episode: Looking for Lucky).
Lucky passes away in the fourth season (Episode 4x09 "Live and Let Die") and the Tanners get a new cat and name it Lucky II.
Trivia
Throughout the series, Alf was warned not to try to eat Lucky. In the first episode (A.L.F.), he asked "Do you have a cat?" when he was requested if he would like anything to eat. In Looking for Lucky, he tried to hypnotize Lucky into thinking he was a bagel, but Willie caught him in the act. In Something's Wrong With Me, ALF said that one of the only ways to cure Melmacian hiccups is to drink cat juice (the hiccups are ultimately cured with raw spinach, a cure that Alf was at first reluctant to mention because it was "disgusting"). In the same episode, Susan has said to Alf, "Anything you do to this cat, I'll do to you" .
Lucky's breed is American short-hair.
ALF's nickname for Lucky is "Luck-meister".