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)

Relevant cards

Note: All applicable cards may not be listed below.
SM5_141
SM5_159
SM5_39
SMA_SV55
SMA_SV55
SM8_121
SM8_203
SM8_223