I've only read of three times that the Tribunal had to be asked to intervene:
Infinity Gauntlet - LT didn't think think that Thanos was doing anything wrong ie. only wanted to replace Eternity (the strong replace the weak) is supposedly one of the oldest canons hence no intervention on the LT's part
Warlock & the Infinity Watch - LT had to intervene because he didn't think Warlock was fit to be supreme being
What if - Korvac obtained enormous amount of cosmic power via Galactus worldship so some cosmic beings asked the LT to intervene but before judgement some cosmics tried to attack Korvac on their own but got beat then absorbed by Korvac. LT's judgement was to kill Korvac via making the sun go supernova (weak I know), Korvac shielded himself and the LT gave up and left.