This isn't an alter ego, this is a separate entity.
Lizzy was one person with smarts and silliness, she hated her smart side due to it being the reason she was picked on at school. She turned to Jupiter for a fix, which he replied, "You look just fine the way you are to me.". Lizzy disagreed still. Lizzy had made a machine to separate her smart and silly personalities. Silly Lizzy and Smarty Lizzy were now present.
However, Silly Lizzy couldn't get along with Smarty Lizzy, claiming she "Ruined her life". Smarty Lizzy understands where she's coming from, since they both have the same memory, so she doesn't fight back. Eventually she moves to a college dorm where she gets Alchemy and Chemistry classes, so she can be just like Jupiter. Now 4 years later, she's back to finally see Silly Lizzy.