|Wuthering Heights (1939) [Heathcliff]: Dies (off-screen) when Merle Oberon's ghost claims him as he's out walking on the moors. We only see a scene of Donald Crisp telling the others in the household how he discovered Laurence's body, followed by a shot of the two ghosts standing on the moors in the distance.
Hamlet (1948) [Hamlet, Prince of Denmark]: Slashed across the arm with a poisoned blade during a swordfight with Terence Morgan; Laurence lives long enough to kill Basil Sydney, then dies in Norman Wooland's arms.
Richard III (1955) [Richard III]: Stabbed to death by the opposing soldiers on the battlefield.
John Gabriel Borkman (1958) [John Gabriel Borkman]: Dies of a heart attack from the excitement of the prospect of starting a new life for himself. (I haven't seen this movie, but have read a summary of Henrik Ibsen's play.)
Othello (1965) [Othello]: Commits suicide by stabbing himself in the neck while cradling Maggie Smith's body in his arms.
Marathon Man (1976) [Christian Szell]: Accidentally stabbed in the stomach when he falls on his own knife after attacking Dustin Hoffman.
Dracula (1979) [Professor Abraham van Helsing]: Impaled through the back when Frank Langella throws him against an iron spike below deck on the ship; despite his injury, he manages to hit Frank with a block-and-tackle which drags him above deck into the sunlight. (It's not clear whether or not Laurence's wound is fatal, but I thought I'd list it just in case.) (Thanks to Michael)
King Lear (1984) [King Lear]: Dies of old age and heartbreak after the death of his daughter (Anna Calder-Marshall).
Sky Captain and the World of Tomorrow (2004) [Dr. Totenkopf]: Commits suicide (off-screen), several years before the story takes place; he only appears as a computer-projected image, and his decomposed body is shown when Ralph Fiennes discovers him in his hideout. (As this movie was made years after Laurence's real-life death, his role consists entirely of old footage edited to fit into the story.) (Thanks to Keenan)