Here are some possibilities:
* Lizzo fans: They are often called "Lizzo stans" or "Lizzo fans"
* Elizabeth Taylor fans: There's no specific name, but they might be called "Elizabeth Taylor enthusiasts" or "Elizabeth Taylor admirers."
* Liz Cheney fans: They might be called "Liz Cheney supporters" or "Cheney fans."
If you can give me more context about who "Liz" is, I can give you a more specific answer.