bobby spray, good evening.
I must admit I have seen a lot of such Cupolas at the top of Scottish stairs in small medium and large so called Scottish Town Houses, really nice features, your one appears in good condition?
Historically, the false light was installed in an attempt in the 60s? to stop heat loss?? who knows?
As for what you do with the holes? how about you make a feature of them? meaning do not simply block out the holes with plasterboard and skim, it will forever be obvious, especially with the down wash of light from the Cupola
If it was me I would fix a feature of some sort over the accesses cut in the Lath and Plaster, something like a MDF "Plaque" over-sised to the largest sized hole by a fair bit, the external face could be "decorated with" beading or moldings to give the appearance of a "Feature" indeed the external face can be decorated any way you want, if possible replicate any main features in any other room? I noted on the Images provided that there are a row of "Dentil" plaster moldings, a similar feature could be replicated on the MDF Panel somewhere in the house? a feature on a plaster molding or similar??
Now for the last bit, these "Feature Panels" no matter how plane or decorative you make them MUST be symmetrical around the slope, that is as above the idea I am coming over with is that the over-sized MDF needs to be placed in a regular pattern, that is if one long wall has one hole, there needs to be two panels, exactly symmetrically placed on the long walls and the short walls, this way it all looks "Right"?
One other thing I suggest you consider introducing insulation on all the slopes to the Cupola, and finally is there any way of considering introduction of insulation to the Cupola itself ?
As above, make a feature of a potential disaster? win, win? who knows.
Hopefully some ideas on what could be achieved?
Please let the board know how it goes.
Lots of luck.
Ken.