Board Thread:League of Legends discussion/@comment-26179768-20170107154440/@comment-1330314-20170107211805

unfortunately doesn't apply on-hit effects, and both and  passives are on-hit effects, so no, it doesn't.

If you want to test for yourself, play a custom game where you lane against a Sion, let him stack tons of health, grab a BotRK and use Judgment on him: if it does interact with Judgment, it should shred his health even if he's at ridiculous values, and if it doesn't, you shouldn't be dealing much damage against him (assuming he also isn't marked as the Villain).