Plastering a badly damaged wall
As commenters have suggested, there are 2 things unusual about your plan:

You're renting this place, and typically repairs on a rental are the duty of the landlord and not the tenant
As tenants, you're unable/unwilling to fully repair the cause of the crumbling plaster (moisture through the wall)

So this advice is for your particular situation, rather than generally advisable to anyone. Other readers will have much better luck and results getting their landlord to perform repairs, as this is their job.
You will quickly have mold problems with any repair unless you properly deal with moisture from the wall. The fastest way to do this is a moisture blocking &quot;paint&quot; such as Drylok. Note that this is not a permanent solution and mold is likely eventually, but these look like open spaces where you can monitor the surface.
Second and slightly better, you could apply sheets of rigid foam insulation directly to these walls and normal paint on that foam surface. The visible cracks and gaps may not be to your liking.
A more permanent and advisable way to cover these walls would be to clear any plaster remaining on the surface, then attach metal studs to the wall, insulate between with rigid foam (NOT fiberglass or cloth-based insulation which absorbs water) and then &quot;drywall&quot; with a paper-free non-nutrient wallboard (here we use Dens-Armor Plus) and then finish with paint.
The key is to not use components which absorb or interact with the continuous moisture you have, or mold will develop and you'll need to replace the surface again in short order.