Not that I am aware of. I can find no information relating to a musical version of King David written by Andrew Lloyd Webber.
Andrew Lloyd Webber however is responsible for other Biblical inspired musicals such as "Joseph and the Technicolor Dreamcoat" and "Jesus Christ Superstar" which includes "King Herrod's Song".
Also note there is a "King David the Musical" but it was written by Tim Rice with music by Alan Menken. (and not by Andrew Lloyd Webber)
Andrew Llyod Webber is still alive and he's a very famous British musical composer.
Andrew Lloyd Webber
Andrew Lloyd Webber
THe phantom of the Opera is his favourite musical
Sir Andrew Lloyd Webber xox
Andrew Lloyd Webber
Bombay Dreams
Andrew Lloyd Webber's Cat's, The Phantom of the Opera,.........etc.
Cats
Yes, especialy The Andrew Lloyd Webber Musical
Christine
Andrew Lloyd Webber composed the musical 'CATS'.