Yes, it would take damage.

Normally, you cannot damage a monster unless the specific rules for the haunt say otherwise). Under the normal rules:

>If a monster suffers
any damage, it is stunned and misses its next turn.

However, the Haunt 21 rules makes an exception to this, it says that while holding the Medallion, you can damage the Zombie Lord. It does not specify anything about physical vs mental damage; so it will just be 1 point of damage either way.

From the traitor's rulebook:

>The Zombie Lord can be damaged only by
an explorer holding the Medallion. Instead
of being stunned, you can take 7 points of
damage before you are killed. Use the
Turn/Damage Track to record damage.
Damage does not reduce your traits.