If my Tyranitar GX knocks out an opponent's Glaceon GX with the "Freezing Gaze" Ability, does Tyranitar GX's "Lost Out" Ability turn on in time for it to send Glaceon GX to the Lost Zone?
Nope, Freezing Gaze is still active when Glaceon GX is KO'd, so Tyranitar GX does not get to use its Lost Out Ability.
Source: TPCi Rules Team (2018-12-27)