Um, Liara, I think something is getting lost in translation here. In the UK our terminology is quite different from that which you are using, and I think things are getting confused.
This might help:
Plaster= the material used to cover interior walls
Render= the material used on exterior walls( on the outside)
Mortar= the material used to glue brick /stone together to build a wall (well, it isn't strictly a glue but that's where it goes)
All three were made with lime until the 1890s. After this, cement gradually became more popular and eventually became virtually universal by the end of the 1950s. Buildings originally made with lime should be repaired/ refurbished with lime- because of the construction technology, if you substitute cement or gypsum where lime ought to be used, you will almost certainly get damp problems.
There are 3 main "types" of lime in the UK:
Hydrated lime, also called bag like or builders lime. Avoid this like the plague, it is intended for use as a plasticiser in cement mortar and is not useable for lime mortars, renders or plaster (unless you want a powdery mess that will fail within months of being applied)
Natural hydraulic lime. This is a dried powder which is mixed with sand and water to make plaster, mortar or render. It is classified by its NHL number. 3.5 is usual for most applications, 2 is suitable for sheltered situations, 5 is used in continuously wet or very severe environments ( lighthouses and canals were made using this for example)
Lime putty (occasionally called non hydraulic lime, but not often) This comes as a putty and is mixed with sand to make mortar or plaster, occasionally render but less commonly used for this. Many lime plasterers consider it to be the best for interior plasterwork, and personally I tend to agree.
Lime putty and NHL lime are a specialist material and only available from a few specialist producers. You won't find it in Jewsons! Similarly, lime plastering is a specialist job and the plasterers do command high wages, which makes it expensive.
For your situation, I would say you definitely need to use lime plaster. The price you said per room doesn't sound too outlandish to me, but it is always worth shopping around and getting several quotes.
Sorry, that is long! But specifying this sort of thing in traditional building is my job, and I can bore for England on the subject! Hope it helps....