In "Better Off Meg", Meg Griffin went to the bowling alley and gave her ID to Bruce, who put her ID with the rest of the IDs in his fishbowl of IDs. When Meg went bowling, she found some dismembered fingers in the holes of the bowling ball she used. Lauren came up to her and said that those were hers from when she went bowling and she needed back so she could put them on ice. Lauren took the fingers and left.
Lauren went to drive to the hospital with her dismembered fingers set beside her in an ice bucket. However, because she was missing two fingers and a thumb on her right hand, she was unable to use the steering wheel properly and ended up swerving off the side of the road and crashing into a telephone pole, which led to the car exploding and her getting burned to death in the accident.
Later that day, Tom Tucker and Joyce Kinney made a news announcement about the incident since it occurred right in front of Tom's apartment. They said that Jane Doe was tragically burned beyond recognition and all that was left behind to identify her with was her ID. This misled them into believing she was Meg Griffin.
Meg saw this on the news and asked Bruce to see the IDs he had left behind. The only ID that didn't belong to anyone at the bowling alley was that of Lauren Wheeler's. When asked how he could have been so stupid as to give Lauren the ID of a girl who looked nothing like her, Bruce admitted that he was high at the time, having inhaled a bunch of bowling show disinfectant, so that must have scrambled his mind into thinking Lauren was Meg.
Later in the episode, Meg was introduced to Not Important and her friend group. Not Important mentioned that they also had an absent friend named Lauren but for some reason, she wasn't returning their texts.