Joe, it depends on where Vaughan Williams went to school, where he went to church, and his own personal preference. I would guess that he pronounced it Die-ves, since I don't believe he was Oxbridge, but since he is dead, we can't ask him.
Dives and Lazarus is Child # 56, so I guess we are safe in calling it traditional- but I can't find it in the DT under Dives. Child attended Harvard, so I would guess he pronounced it Die-ves. I have posted a Negro spiritual version (thread 9673) which shows in the threads. Lots of songs about low dives, however. If I enter Dives, or Dives and Lazarus, I get the Murder of Maria Martin (now is she Ma ree a or Ma rye ya? - I pick the former).
Putting Lazarus in the Forum turns up "'Divers' and Lazarus" (which seems to be var. #5, Diverus and Lazarus, in Child). A spelling check is needed here. Since Vaughan Williams died in 1958, his arrangement of the old song is still probably copyrighted somewhere.