Inspector Lestrade is a holodeck recreation of the Scotland Yard detective from the Sherlock Holmes stories, who brings Data's Holmes a murder to solve.
Lestrade appears in Elementary, Dear Data. He is part of the Victorian London setting in which Data plays Sherlock Holmes with Geordi La Forge as Watson.
After Doctor Pulaski wagers that Data cannot solve a mystery he has not already read, the computer is asked for an original case. Lestrade calls the detectives to the scene of a killing in a dark street, where the baffled inspector watches as Data reads the clues and names the culprit within moments.
The investigation is a sideshow to the real problem. In phrasing the request, La Forge has asked for an opponent able to defeat Data, and the computer has responded by giving the hologram of Professor Moriarty an awareness of the ship.