Does she really like human flesh?

We are beginning to wonder if our youngest 2 year old (since both Lizzy and Anna are 2 right now) likes the taste of human flesh! Lizzy being the smallest has decided that "biting" is the best option to get what she wants from her sisters. Today she has broken the record (at 4pm and the day isn't over) and bitten 3 times, 2 to poor little Anna and 1 to Emma. This past weekend she surpassed her total record, I can count the bites from looking at her poor sisters bruises on their arms and legs! Wherever we go I feel the need to explain why Anna has bruises in the shape of a cirle all over her for fear someone will think it was Jody or I! We have tried almost everything (the almost is the one thing we haven't tried that will work) to get her to stop and luckily she has only bitten her sisters, Jody and I. We've tried spanking, putting her in timeout, I even resorted to biting her back, but she only laughed. She knows what she did was wrong because shortly after we hear a scream of "Lizzy bit me" we hear "Sorry, Anna" (even if it's Emma because she's gotten so used to saying sorry to Anna). Does anyone else have any suggestions from another "chain-biter"? Any advice Anna & Emma would greatly appreciate!