It has been mentioned that the melody used for Dives and Lazarus, LAZARUS from English Country Songs by Lucy Broadwood and Maitland, 1893, is also The Star of the County Down. I did some research on the tune family Lazarus, which has already been pointed out, includes the very old Gilderoy. The oldest variants of the tune I found were a Gregorian chant, En Gaudeat, 12th Century, a Latin Carol called Congaudeat, 1582 which takes us to Gilderoy then Lucy Broadwood's Lazarus and finally The Star of the County Down.
This is of course a quick summary .