Lizzy is a minor character that Penny sets up with Raj after he has a disastrous "date".
Biography
In "The Itchy Brain Simulation", after Raj receives devastating news that Lucy was seeing someone during their "date", Raj throws a fit at Penny, Penny then responds that she can set Raj up with a girl from the Cheesecake Factory. Raj later on goes on the date which initially started well, with Raj complimenting her. It all started going downhill after Raj throws another fit when he doesn't believe that she doesn't have a boyfriend, It gets worse when Raj suggests that he can be the other man if she wants a little "something-something" on the side. Presumably, the date ended there. Lizzy screams at Penny, yelling "What is wrong with you?!", this act reciprocates with Penny yelling at Raj the exact same words and ends at Raj yelling at himself in the mirror.