He is the same form as Plankton, but has a large beard, a light orange-yellow waistcoat, and a white shirt.
When SpongeBob thinks he is seeing killer Krabby Patties, he goes to see Dr. Lankton. He is actually trying to get SpongeBob to tell him the secret formula. After many failed attempts, like using hypnotism and an ingredient combination, SpongeBob feels better and goes back to the Krusty Krab. Dr. Lankton yells "No! It's a lie! Therapy doesn't really work. You're still sick! Very, very sick!" but it doesn't work.
The name Peter Lankton has the "P" removed from "Plankton" and made into Peter.