I think I've gathered enough material for a few posts on the use of King Lear in films that aren't King Lear.
The first of them comes from a pair of alert readers. They let me know that there's a scene in The Madness of King George in which King Lear plays a prominent role. When films are made about British Kings, Shakespeare has to be there (cf. The King's Speech, for which, q.v.).
This scene is very nicely layered and quite moving. The mad king (recovering a bit from his madness at this point in the film) plays Shakespeare's greatest mad king (also recovering a bit from his madness at this point in the play).
Links: The Film at IMDB.