Common:
* Lex
* Lexe
* Lee
* Lexi-Lou
Cute:
* Lexie-Poo
* Lexie-Belle
* Lexi-Cakes
* Lexie-Bug
Quirky:
* Lexa
* Lexie-licious
* Leela
* Lexi-licious
Other options:
* You can also use the full name Alexandria and shorten it to Alex, Ali, or Sandy.
* If the full name is Alexandra, you could also use Allie or Allie-Cat.
Ultimately, the best nickname for Lexi will depend on her personality and what she prefers.