What happens if a lead actor dies in the middle of filming a movie?

If a lead actor dies in the middle of filming a movie, a direct appoints a new actor for completing the movie.

Well, it really depends on how far along the movie is and the equipment the studio has available. In say, Heath Ledger's case, there was still a few shots left in the Dark Knight that he had not completed but Nolan used some clever editing and a stand in and got the job done. For Ledger's last movie, The Imaginarium of Doctor Parnassus, Gilliam simply didn't have the screen time with Ledger to stick to simple editing. So, they put in rewrites and had Johnny Depp, Jude Law, and Colin Ferral finish the movie potraying different transformations of Ledger's character.