HEADS UP! MISSABLE ACHIEVEMENT!
This achievement occurs after your battle with Mr. Giblets. You get back home to find your sister has gone missing and Gene sends you to go find her. You'll of course head to your favorite Space Applebee's in the slums. When you get there you end up having a "heart to heart" confession with Kenny and are served by the staff throughout the conversation. At the end of the conversation you'll notice Lizzie outside with her boyfriend.
KEY POINT! Before departing, ensure you glance down at the table, settle the bill, and then leave.
If you don't.... you'll have to start all the way over from the beginning, there is no way to jump back to that part in the story.