Flights from NYC disembark into level H. From there you can get to level G by carefully turning left after passport control. Note that you are in Schengen now. The Atlantic lounge in T1C is non-shengen, so even if you manage to find the T2-T1 bus, I doubt it will drop you in T1C. AFAIK it goes to T1E.

I would call the Atlantik lounge and ask if they will let you in:
http://www.munich-airport.de/en/cons...ntic/index.jsp

Alternatively, why not take a day room in the onsite hotel? If you are arriving on LH its available at a rebate. The regular rate is 150€
http://www.kempinski.com/en/munich/h.../day-use-room/

The MUC airport showers are fine. This is Germany after all.