The problem with NHL
This won't take long...except I got distracted and went off on a tangent waffling about strength.
NHL isn't as porous as the vast majority of original mortars and plasters.
Plaster is layered, 1:3, 1:2 and 1:1. Because the more lime, the stronger the pull it has on water. So you want more lime on the surface that you want it to dry off of. Ie. indoors your plaster will absorb vapour produced from your day to day actviities until the RH drops or a lot of air movement is present. The layering pulls the moisture to the surface where it turns to vapour and becomes one with the atmosphere, as it were. Outside is similar but the earth goddess Gaia provides the moisture rather than the hoi polloi.
So when you apply NHL3,5 for example its like you're putting 1:6 over 1:1. Why you say? Because NHL's contain lime AND clay, the percentage of which differs depending upon brand and class. But even NHL 2 has 20% clay and that then consumes 20% of the lime, leaving only 60%. And they are often used at 1:2.5, meaning that instead of 1:1 like the original mortars they are approx. 1:4 in a best case scenario.
The result is that moisture can be pulled backwards of the wall heart is dry. Think about it like this: you have a wet sponge, on each side is a wet/dry vacuum cleaner but one is stronger than the other. obviously the water is going to go to that vacuum and not the weaker one.
Now this, I must confess, is very reductive. However if this is an issue you will already be aware of this fact and have no need to use this information. This is a general rule for people who are confused by 'lime'. However as a second caveat, do not trust suppliers or trades who say NHL is fine. I'm talking about conservation professionals not someone who financially benefits from it being NHL.
I say this because there are some applications or scenarios where this rule might not apply but very few and very unlikely to be applicable to vernacular works.
Strength is in comparison to the original mortar because of the effects of different thermal dilation rates. If you put something strong on the surface that doesn't move about and the rest moves about a lot and is soft, then it will obviously cause issues, the binder strength itself is also an issue. Arguably a bigger one, I mean the strength of adhesion. People concentrate on compressive strength which is almost certainly going to be weaker than the building units in most scenarios. Sandstone is 20+N/mm2. 'soft' bricks are 10N/mm2 and those are the inside ones not the exterior bricks. Old facade bricks are higher getting up top 20N/mm2. Nori's and other engineering bricks are 50-100N/mm2.
The biggest shame about all this is that if the NHL's were fired at traditional temperatures it would produce pozzolans not hydraulic materials out of the clay. Resulting in a much more porous material. But they don't and they are unpredictable because of it. the firing range produces different amount of hydraulic components. It's harder to store and use like that too. Same with CL90 tbf. Some quicklimes are lower fired but not many. Different flocculation resulting in different porosity and curing speed because I know someone will want to know the difference in firing temperatures of air limes.
In summary:
NHL's are usually micro porous to mesa porous and air limes are mesa porous to macro porous. And that's what determines breathability. In some scenarios this isn't true but 'better safe than sorry' is simply good working practice. Why would you bother testing it or taking the risk when there are safe options available like using low fired brick dust as a pozzolan which retains mesa and macro porosity and has a low upper strength limit.