Whether stone is a good candidate depends on absorption. Hard stones such as granite, and anything sealed in the past, absorb very little, which leaves the lime with a weak hold. Dropping water onto several stones shows which you have, which is worth knowing before choosing a finish.
A north-facing wall that stays damp and mossy raises a second question: why? Cleaning it and letting it dry out is the start; the lasting fix lies in gutters, ground slope or splashback, so the lime can release moisture the way it should.