To me, the darkening/lightening seems to suggest that the spots are getting wetter and dryer - and pretty rapidly, too. Are you able to associate this colour change with rain?
Alternatively, what is in the room above this wall? Is it by any chance a bathroom?
Tracy - I've posted again above, but I'm a bit behind the times with this thread!
If the spots definitely darken when it rains, then there can be little doubt that rainwater is getting in somewhere. However, as the wall is lath/plaster it may not necessarily be entering anywhere near the offending spots. Water can be a devil like this - it can get in somewhere a long way away from where it appears. So you'll need to do some really wide-ranging detective work.
Personally, I wouldn't start hacking through the plaster where the spots are. As the plaster is applied to laths, then it is presumably isolated by a cavity from the stone wall, in which case - as I've said above - the spots may be quite a distance from the point of water entry.
In your shoes I would still be concentrating my attention on the wall outside - look for cracks in the rendering (not necessarily right where the spots are), leaking gutters, flashing, etc. etc.
Thanks David, this is really useful. I can confirm that the spots usually (not always) darken when raining. There is a bedroom and not a bathroom above the room where the spots are showing so I guess any water must be coming from outside rather than inside. Therefore before any hacking commences I will have a more detailed look at the outside wall, and make sure that my search is far reaching and not just in the corresponding area outside from where the spots show themselves inside. Thx.