If Elder Dragon is killed during damage assignment of a combat showdown (after consecutive focus passes), does the passive still cause my unit to die?

Yes, Elder Dragon’s ability continues to apply to enemy units even if it is killed during the same combat.

According to RiftJudge FAQ #8684, the ability functions as long as your damage is dealt to enemy units. It does not require Elder Dragon to remain on the battlefield after damage has been assigned.

Reasoning

1. Scope of Ability: Elder Dragon’s ability text states: "Any amount of your damage is enough to kill enemy units." Both conditions (the source being "your" damage and the target being an "enemy unit") are evaluated at the time damage is assigned.
2. Combat Timing: Once combat damage is assigned, the ability validates that the criteria are met. If Elder Dragon is removed from the battlefield during the combat damage step, the modification to the lethal threshold for enemy units remains in effect for the damage already assigned.
3. Persistence of Effects: Because the ability modifies the rules of combat damage for that specific instance, the state of the Elder Dragon at the conclusion of combat does not retroactively negate the damage already dealt to enemy units.

Note: I could not fully verify this ruling against the retrieved rules.