If you’re flying premium economy on Lufthansa out of EWR to MUC, that ticket alone does give you access to the Lufthansa lounge, even if the booking was made through United. What matters is the operating airline and the cabin, not who sold the ticket.
That said, there is always a small risk of access restrictions if the lounge is completely slammed. It’s less common for airline operated lounges than for third party day passes, but it can still happen. Lufthansa tends to prioritize their own premium cabin passengers first, so you’re in a better position than someone trying to buy access at the door.
With a 5.5 hour layover, staying airside and using the lounge is probably the right call. Leaving the airport would be tight and stressful, especially with re clearing security.
I’d do the lounge and just settle in. Way less hassle
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