Mike the lunatic is the young man whom Phoebe suspects of being a lunatic and stalking her family. She first encounters him right before her mother disappears: he visits the Winterbottom household and asks to speak with Mrs. Winterbottom. He seems nervous, and when Phoebe begins to see him lurking all over her neighborhood, her imagination gets the best of her. She believes he is responsible for leaving the secret messages on her doorstep, and she thinks he has kidnapped her mother.
She and Sal decide to track down this dude. They discover he's a student at the local university. When they reach the university, they find Phoebe's mother is there too, talking to him. She has not been kidnapped. She is having a good time with him on campus. She kisses him on the cheek.
Eventually, Mrs. Winterbottom returns home, bringing Mike the lunatic with her. She tells her husband and daughters that Mike is her son and that she gave him up for adoption a long time ago, before she married Mr. Winterbottom. Not only does Phoebe get her mother back, but she also gains a brother. Whether she likes it or not.
Honestly, we don't know much about Mike himself, other than the fact that he's Sergeant Bickle's adopted son, and he's a student in college. One thing we do know, though, is that Mike is an example of how Phoebe's imagination can get the better of her, making her believe things that aren't true or real.