I don't think I need to; the lvl 60 version started dropping when I was only lvl 27. Is there a limit to Luck benefits?
EDIT: I hadn't completed all the side quests because I was speedrunning through, but the Abyss stopped my lvl 31 with lvl 62 enemies. I'm going back through them in order, and the above-mentioned bug has only occurred once so far, in Southwark.
This is the image of Pratch's dialog after completing Medical Necessity, and the "Choose For Me" button did not respond. After clicking the X box, the quest was removed but my palladium and exp were unchanged.

EDIT: Happened again for Claire's "Even Stephen" quest.