Besides On Stranger Tides, I feel on fairly safe ground in surmising that George MacDonald Fraser's satirical pirate novel The Pyrates was something Ron Gilbert read while brainstorming MI1 - mainly because the book's hero is a dashing Royal Navy man named Ben Avery, meant to be a younger version of the infamous historical pirate Henry Every, who seized the Mughal Emperor's treasure ship Ganj-i-Sawai (along with its escort ship the Fateh Muhammad), packed with many of the Emperor's close relatives who suffered great violence, while the ships were sailing back to India from a pilgrimage to Mecca. What happened to the real Henry Every after the raid is uncertain; as far as can be surmised, he seems to be one of the rare pirates who "got away with it".
The early design documents for MI1 describe the protagonist (then called "Smear West") as a pirate who seized a treasure fleet and then became a has-been from retelling the story a bunch of times, much like Guybrush in MI2 with killing LeChuck. That detail as presented in the design documents seems to be specifically modeled on Henry Every's career (few pirates ever seized prizes as rich as Every's), and the idea of seeing such an otherwise famous protagonist at different times in his life feels like something Gilbert might have picked up from Fraser's novel (though in this case taking inspiration from the unknown "after" of Every's career rather than the "before").
The early name of Largo LaGrande, "Lord Jack", also suggests a possible connection with Joseph Conrad's novel Lord Jim, about a disgraced sailor who ultimately finds redemption through death. Whatever bearing such a story might have on a planned storyline for Largo I couldn't say.