NCE is a third party lounge (i.e. not run by BA) but you'll have access on a CE ticket. It's also - IIRC - a Priority Pass lounge.
Note that once you get into the gate area (where the lounge is), you can't get back out and - IIRC - there's only one cafe and one shop!
It didn't always used to be like this. I remember a few years ago looking to book CE with BA to and from NCE when I was a lowly Blue, I found out that CE PAX had no access to the lounge only Golds and Silvers. I booked with BD instead, saved a little money and had lounge access.