Need to cover a façade with lime. Should PVA be used as a binder?

My façade is highly absorbent of water. I think the water even passes through the wall (effectively a leak). I plan to render some lime on top of it. It’s the kind of lime that turns to chalk if it oxidizes over the span of a year. The stuff I have is about a year old, so I have to use it up anyway.

Should I “paint” a layer of PVA (wood glue) on the façade first to help bind the lime? Then should I mix some PVA in with the lime? Or would that choke off the breathability?