Lime mortar is naturally flexible MAK. Our 1830 house is held together with it. It allows for any ground movement and as such is weak. The builders here use a 'fake' version on Listed Buildings and in Conservation areas with a mortar mix of building sand, sharp (washed) sand, cement and lime which has the appearance of a traditional sharp sand and lime mortar with near the strength of a modern cement mortar. Trouble is I can't remember the exact mix volume ratios but I think it was something like 5 building, 3 washed, 1 cement, 1/2 lime. Bit odd really as cement reacts badly with lime when it is dry and cracks -my floor skimming went 2 days after it had dried! Cracked and lifted all over. Needed tilers (expensive) sealer -3 coats and then relaying.
Guess you need to test a bit MAK to see if you get a reaction. Stone is limestone in that area isn't it?