The year of the rendering suggests that it may have been done traditionally, i.e., by nailing up panel/reed or other reinforcement and throwing the mortar directly on. Later, the technique came with nailing up thicker insulation boards and throwing the mortar on them. But an air gap doesn't sound like a solution for rendering an old house in the 50s.
When it comes to stucco facades, there is a difference between single-stage and single-stagesealed. Older houses, as Clas writes above, have stucco on splinter panels, reed mats, spikes, or similar materials and are in that sense made in one stage, but can breathe.
The mistake that Myresjöhus and others made is using dense XPS or similar as an insulating intermediate layer and stucco substrate directly on the wooden frame. As known, it didn't go so well. Then it became single-stage sealed.
The mistake that Myresjöhus and others made is using dense XPS or similar as an insulating intermediate layer and stucco substrate directly on the wooden frame. As known, it didn't go so well. Then it became single-stage sealed.
Plank frames often had an asphalt felt on the outside of the frame, a so-called förhydningspapp. In connection with rendering or facade bricks, a denser underlay felt was often used. The important thing is that the plaster and what's supporting it can breathe outwards.
That was a shame 
OK. Even though it is more work and effort, I strongly recommend knocking down the plaster, the mat, and possibly the cracked panel, and then building a moderately thick layer with insulation+panel.
This way, the roof overhangs and similar features retain their lengths and proportions.
This way, the roof overhangs and similar features retain their lengths and proportions.