Boy Who Shattered Time

What happens when I play Ekko, Boy Who Shattered Time's activated ability, play a unit, and then play Unlicensed Armoy's activated ability? Will the unit be killed on my next turn?

Your unit's death from its triggered ability will be replaced by Unlicensed Armory. Although the unit has the text "Kill me at end of turn." appended to it, that text is synonymous with "Kill me at the end of this turn." On subsequent turns, it will not trigger.

When "at end of turn" appears on card text, it is used synonymously with "at the end of this turn." Although granting that text to a unit is strange, it isn't outside the bounds of possibility. If the unit remains on the board after the triggered ability resolves, the condition for its ability to trigger will no longer be able to be fulfilled, so it will not trigger again. If the unit changes zones to or from a non-board zone prior to the triggered ability triggering, all of its temporary modifications-including this granted text-will be removed. As such, the ability will no longer exist to trigger.

Relevant rules: 359.3.e.16., 124.1.