Your original mortar joints are indeed lime-based, so going back to lime is a good idea, but watch out for making the opposite mistake: 100% pure lime mortar can be too soft for some areas. What really works well is a lime-cement mix in the right proportions (like 3 parts lime to 1 part cement) - it gives you the flexibility and breathability of lime without losing the strength you need. The key thing is to avoid pure cement alone, which is too rigid and will crack the old stone over time, but lime alone risks wearing out too fast depending on your façade's exposure.
Honestly, if you're not totally sure about your ratios, you can also find ready-made restoration mortars (they make these product lines specifically for old houses) that already have the right formula in them. Before you get started, test a small inconspicuous spot to see how it behaves with your specific stone.