Is "Archon of Justice" exiling a target permanent when it dies an example of a lapsing ability?

The situation described with "Archon of Justice" does not exemplify a lapsing ability. A lapsing ability typically refers to one that, after being triggered or resolved, does not persist in any form into the future rounds of play unless re-triggered. Instead, the ability of "Archon of Justice" to exile a target permanent when it dies is a one-time effect that occurs at the moment the Archon leaves the battlefield, resolving immediately rather than persisting afterward.

In contrast, the other options provide different perspectives on the ability. The idea presented suggests that because the ability targets an opponent's permanent, it might be classified differently, but this targeting does not influence the classification of the ability itself. The key aspect here is that its effect occurs once and does not remain on the battlefield or continue to have an ongoing influence, which supports the reasoning for recognizing it as a one-time effect rather than a lapsing ability.