The Godfather, Part II and The Lord of the Rings: The Return of the King are the only two sequels that have won an Academy Award for Best Picture. All films in The Godfather and The Lord of the Rings trilogies were nominated for Best Picture.
The first sequel nominated for Best Picture was The Bells of St. Mary's. While The Silence of the Lambs was technically a sequel from a plot standpoint, a completely separate production company, studio and cast were involved in the film's production. The Lord of the Rings: The Return of the King is the only third part of a series to win Best Picture. Other sequels that have been nominated for best picture include Mad Max: Fury Road and Toy Story 3.