Lizzy is already a nickname. It is traditionally a short form of Elizabeth / Elisabeth.
Some common nicknames for Lizzy are Liz, Lizzie, Eliza, or Beth.
Liz or Lizzy
lee lizzy essy lala
Lizzy Plimpton goes by Liz, and Lizzy.
Some common nicknames for Lindsey are Linds, Lin, or Linnie.
Elizabeth Mulkey goes by Lizzy.
Elizabeth Jagger goes by Lizzy.
Elizabeth Lind goes by Lizzy, and Liz.
Elizabeth Kimball goes by Lizzy, and Liz.
Lana Del Rey goes by Lizzy.
Elizabeth Del Re goes by Lizzy.
There are lots of nicknames for Alison.. :3 Ali (Ally) Al Alice Liz Lizzy Hope that's helpful :]
Tia Lynn Ballard goes by T-Bird Lizzy.