Originally, fortuitous meant "occurring by chance," as in "Their fortuitous encounter on the train was the beginning of a lifelong friendship." The word derives from the Latin fortuitus, a deriviative of fors, the noun meaning "chance" or "luck."
There is nothing specific about good fortune in this sense, but the fact that fortuitous sounds like both fortunate and felicitous (meaning "happily suited to an occasion") likely caused a shift in meaning to something closer to fortunate ("bringing some unexpected good").
After both goalies were stellar throughout the contest, [Nick] Leddy scored a fluke goal when his backhand pass went off the stick of Flyers defenseman Travis Sanheim and through the legs of goalie Brian Elliott. “I think it was more of a fortuitous bounce than anything,” Leddy said.
— Associated Press, 18 Apr. 2021