Why paint a British roundel on a non-British Lynx?
Best guess; the photos are from the delivery flights in the 90s. The helicopter in the photo has the same registration as when it was first delivered (ZH583) and has not been active since. 
Update: Although I'm having problems finding an authoritative source, it looks like the registration was resurrected for test flights post-upgrade. Mark Youd has taken a few photos of ZH583 recently(flickr), it was listed in the April update from a site called &quot;Military Aircraft Markings&quot; and looking at various planespotter forums and various flight tracking sites(1)(2) you can find multiple reports of flights being undertaken using the original ZH583 registration.
The roundel and registration is temporary and easy to remove, but was required for the test flights in the 90s as well as prior to delivery post-upgrade. Looking at other photos you'll see the Portuguese registration on the tail; on your photo this area appears to be covered up to avoid having an aircraft with two different visible registrations during test flights.
As for your hypothesis; the second is totally off target. There are loads of barriers in place to avoid having any situation involving a trigger-happy fighter pilot, such as predefined rules of engagement and procedures civilian and military control centers follow.
My guess is that the first one is closer to the truth; although I haven't found a source for it, I can imagine that it would be easier for the factory and the test pilots undertaking the upgrade and test flights to schedule and log flights using the UK registrations.