The power of the Infinity Gauntlet doesn't seem to worry The Living Tribunal
TLT has shown no worry over the power of the Infinity Gauntlet. As you noted he was not worried about Thanos taking control of it and challenging Eternity and in the aftermath of that event he made Adam Warlock split them.
That seems logical if we consider that while the Infinity Gauntlet has the power to end and recreate one universe and its Cosmic Entitites, The Living Tribinual is one for the entire Multiverse.
The Living Tribunal may or may not have been defeated when Thanos claimed the power of Heart of the Universe in The End, when he absorbed the Living Tribunal, because Thanos only absorbed and recreated a single universe, whereas the rest of the multiverse suffered no effects from his actions, it was likely just a Manifestation Body/weak avatar of the Tribunal.
This interpretation was validated by Marvel's executive editor Tom Brevoort, who stated that like all, "The End" series, the story was intended to have no effect whatsoever on continuity.