There is no relation to class, AFAIK. People have noted differences in luck in different games, but I don't think there was any correlation with class.
Item quality is partly dependent on character level, however. The higher your character level, the better the chance you have of an item's stats being in the upper range for that item.
For example, in a game to try for the lowest level finish, Ariana reloaded a large number of times trying to get a holy weapon with Frost around level 5, but failed. Returning at around level 10, she found it much easier to get a better sword. She hit the gong on level 12 (ending up in the wastelands at 17), then quit.