It would be normal to remove the wheel. It could be replaced without, but it would make the job more difficult than necessary. See this video.
Par for the course for some garages though. Main Volvo dealer claimed not to have removed my wheels when they lost two wheel nut caps, despite having already sent me info0rmation that would have been impossible to obtain without, plus a video of the car with the wheels removed.
Another garage told me that my wife's locking nut was seized and had been damaged trying to get it off. I had loosened and retorqued it to spec only a couple of hours previously. What the mechanic meant, after bull**** to english translation was, "I'm a lazy sod and tried to get it off with an impact gun but the wheel nut key slipped due to the torque".
When I took my wife's car for a new tyre last week, I removed the lock nut first and replaced it with a normal nut, then swapped them back when I got home. Never had any issues with the tyre company I use, but after so many poor experiences of so called mechanics I am now forearmed!
Depending on the lock nuts you have, it might be possible to obtain a single replacement, or it may be cheaper/only practical to replace all four. There may be a code on the key, some aftermarket keys can be identified and a replacement obtained by sending an image to the distributor, others may have a code on the box, etc.