Pointing with Lead Mate: what to use to pack joint?

Personally, I wouldn't bother with the Lead Mate, and just use lime mortar for all the re-pointing. If you have some to hand, you could use that.

How long is the flashing? I'd be a *bit* concerned about the structural integrity of the wall with a long deep slice raked out of it. Filling the rake with flexible sealant doesn't strike me as providing much strength, so I would want some sort of mortar. (and I'm a great believer in not using cement mortar on lime-mortared walls).

It's the parapet wall above the join between the two sides of the rear extension: 7m long* by 3 courses plus capping stone high (except around the chimney stack which has been reduced to 7 courses plus flaunching).

I take the point about lime mortar but I doubt that'd have enough flexibility to cope with the seasonal movement we are getting - quite possibly adding to the inevitable differential thermal movement. (There's also longer term movement - ie subsidence - but that's another and of course bigger problem.)