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Yes, you will need to clear security when going from Terminal 1B to Terminal 1C. The non-Schengen Skyline train station in 1C is outside of security, and requires you to pass through security in order to get to the C gates. Presuming the lounge you are considering accessing is past immigration (I'm presuming it's the LH lounge at gate B42, which is) then you will not need to clear immigration again to get from there to 1C non-Schengen departures.
The best way to answer questions like this is to download the Lufthansa app, which provides an excellent map and even with step-by-step instructions between any 2 points in the airport - including listing immigration and security checkpoints.