Answer
These placeholders are called Context Substitution Variables, and they're explicitly defined — not automatically available for every conceivable user attribute — in a dedicated Context Substitution Variables configuration screen. The default-site placeholder works because it's set up as one of these defined variables; a default-coordinator equivalent typically isn't set up as a Context Substitution Variable by default, which is exactly why it doesn't resolve as a Lobby parameter even though the underlying data itself is correctly configured for the user. If you need this specific variable, it would need to be added as a Context Substitution Variable there.