Once an elite troop’s die value reaches zero, they are removed from the map and returned to the player’s faction mat, available for purchase once again.
When deploying an Elagynt elite troop, does the Lythe basic troop has to be deployed in the same region?
Yes
Yes, they get deployed together. Usually, unless stated otherwise, deployment happens to the shores, so both would go there. But if an action, ability, or scenario allows you to deploy an Elagynt directly to a region, the Lythe would go with it.