Even if LX First Class Lounge in Zurich would not be accessible to you, as you are traveling on a Star Aliance Carrier in First, you have access to the Star Alliance Gold Lounge, which is the Senator Lounge in ZRH.
Then there is the rule that LX and LH F BPs allow you access to LH/LX First Class faciities for the day of your travel.

You should reply to that mail and ask them to check there info.

http://www.swiss.com/web/EN/services...zurich_lounges clearly states LH and LX F tickets as valid for acces the ZRH FCL.