Yes lime is more breathable than cement mortar (particularly when the roofers use 1:4 cement: sand mixes). The purpose of a lead flashing is to keep water out. The main reason they fail is because they aren’t dressed far enough into the mortar joint (25mm is a minimum if the bricks are porous or exposed locations 35 of 45mm might be more appropriate) – the idea is to intercept water soaking into the brick during a storm to direct it back out of the wall. In places like chimneys this might not be enough and you need a top hat dpc in addition to the flashing.
People get hung up on lime, if you ask a builder or roofer to mix and place lime mortar without prior experience they will almost certainly mix it too wet and won’t tend it as it cures, which will then crack and fall out. I’ve worked with a number of the people who wrote the Historic England text books on mortar, leadwork conservation etc. At least one of those recommends that you chat out joints for flashings to 40mm fix the flashing and then seal the back of the joint with leadmate then post the front of the joint with lime to keep everyone happy.
The pointing to flashings is a nightmare, particularly on the southern side of buildings, even when it is done by people who know what they are doing. Personally if it was my house and it wasn’t listed I would for leadmate every time.
If you do go for lime mortar and you want to do it properly cover the lead which is dressed into the joint and which will be in contact with the lime with a later of masking tape. The free lime in a wet mortar can attack the lead, it won’t do much damage but it can roughen up the surface enough for the lead and mortar to stick together, which can make the mortar more likely to crack as the lead expands and contracts. Its not proven but I trust the experience and skill of the contractors who swear by it.
If you want to be really on trend, use hot mixed lime (according to the true acolytes hot mixed lime cures all problems, including world poverty).