If you intend to undertake the restoration yourself, be prepared for a difficult and time consuming task. In places where sizable areas of plaster are missing right down to the wooden lath, pieces of sheet rock cut to fit and attached to the lathing with drywall screws is probably the easiest first step. Smaller holes can be filled with joint compound. Areas of crumbling plaster need to be removed back to sound areas,

Finishing the whole wall smoothly is not easy. Fiberglass mesh comes in 3 to 4 foot wide rolls. This has an adhesive on one side so it can be applied to the wall like wall paper. After that, it's layers of joint compound sanded and smoothed between coats, followed by primer and paint. The trouble with using joint compound is that it does not provide a hard surface like finish plaster, so it is prone to damage. Using actual plaster is not a DIY project. Plastering is a highly skilled trade that takes years to master.

There used to be a product called Nuwall - not sure if it's still on the market. This was a fiberglass cloth applied to the wall and then impregnated with resin. Left a hard, durable coat, but was never as easy to do as the manufacturer's directions implied.

So, it might be useful for you.

from their advice sheet:
An acrylic copolymer resin, with excellent alkali resistance and adhesion to masonry surfaces.
Usage: For use on interior and exterior masonry and plaster surfaces which are porous, chalky or
lightly degraded but otherwise structurally sound. Provides a well-bound and durable base.

Disclaimer: I'm a huge farrow and ball fan, but I like Ellen Kennon too. Not affiliated with either co.

Straight lime putty was not commonly used in the US for plastering, mostly because of the very long cure times.
A mixture of lime putty and gauging plaster was a common mixture.

The base coat (brown coat) was lime putty, sand, horsehair, and gauging plaster.

The second coat (scratch coat) was lime putty, sand, and gauging plaster. The surface was textured when partly set to provide better mechanical bonding for the finish coat.

The finish coat was lime putty and gauging plaster.
Layers were added when the lower layer was set, but not necessarily dry, to facilitate binding.

If the surface dried (like over a weekend) it was dampened before the next layer was applied.

The curing time is around a week in a heated space, and after that it can be painted.

Bonding to old plaster with Easysand or Durabond often fails since the old material is very dry, and pulls moisture from the new preventing it from curing correctly (Easysand and Durabond cure by chemical reaction, not drying out like pre-mixed joint compound).

There are also binding agents. Many are polyvinyl acetate based the same as Elmer's Glue.
They are applied to the old edges and allowed to dry until tacky.

Old plaster walls intended to be papered may not have a finish coat, but a smooth scratch coat.
It is not hard to place a finish coat using bonding agents and modern setting joint compound.
A plasterer's trowel makes the job go much faster than trying to cover the large areas with a drywall knife even a wide one).

One thing often missed in plaster work is the use of retarders to slow the setting time of the plaster.
High temperatures and can result in very short setting times unless retarder is added to the plaster/lime mix.
Simply adding more lime usually extends the setting time excessively.

"Plastering" by Sawyer is a standard text.