Woodfibre with a lime plaster is good for these sorts of historic walls with no DPC. 20-80mm depending on space and moisture load. There are several vendors of suitable boards. No idea what is available in Hungary, but the manufacturers I am aware of are in Poland (Beltermo, Steico), Germany (Gutex, Steico (HQ), Udidammsystem), France (Pavatex, Steico), Norway (Hunton).

You can get boards with a squishy back for irregular walls (Udireco) but normally you parge the wall first to get it vaguely planar, then glue the boards on. UdiNF are relatively small in order to flex a bit for irregular walls.

80mm is generally reckoned to be as thick as you want to go on single-skin walls of unknown dampness. 60mm is playing it a bit safer. But even 40mm will make it much nicer.

I've seen 80mm put on a sandstone historic building (sandstone block, rubble, brick inner ~400mm thick) and that worked very nicely, even when they had a massive internal gutter leak saturating the wall and woodfibre for a month or two: It dried out again remarkably quickly (once the hole was unbunged) and nothing bad happened to the wall surfaces (which I think is an excellent illustration of how robust a system this is).

I take the point about battens but without battens how can the VCL be fixed to the warm side of the insulation and then plasterboard (or other finish) be fixed?

Cork would fail in this situation, one on price, way more expensive than EPS and the other problem is that if it is left as a feature (nice idea) it would not be robust enough to withstand e.g. the tenants puppy brought in against the house rules or the errant child who decides it would be fun to pick bits out of the wall

We are in a similar situation with one wall, although on a house. Regarding boundary issues you are entitled to access via your neighbour's property/curtledge to maintain the outside (free Party Wall agreement) ie you can replace roughcast if needed or remove a band 300mm or so high and replace with thin XPS plinth then re-render to keep out water if it's needed (just done this for our wall which is right on a road that often has water running down it. XPS was suggested by Ecological Building Systems- the Diathonite supplier- the inside of this wall is below ground and obviously no floor insulation and plaster inside is blown.

If you want the walls to be able to breathe (vapour open) as lime does then the exterior render needs to be breathable ie not cement render ... for this internally you will need to level the walls to avoid having air gaps behind IWI, diathonite thermactive is both insulating and suitable for levelling and it's lime based. No need for battens.

Insulation is either flexible eg cornerstone insulating plaster or if you can afford it aerogel (there's an aerogel plaster product - https://www.backtoearth.co.uk/product/super-insulating-aerogel-plaster-fixit-222/ - and you can get Aerogel Wallboard which has battens built-in), or alternatively you use rigid boards eg Wood like Gutex or Lime Green's Warm Shell. On top of that you need either a "breathable" plasterboard or lime plaster- hence suggesting cornerstone insulated plaster, PLUS breathable primer and breathable paint suited to lime. If you want fairly thick insulated eg layers of Diathonite then there's a mesh needed but it's simple to do. Everything going into the wall will need special thermally broken fixings instead of metal screws. Often that means radiator fixings, electric cupboard or meter, skirting board can be fixed with adhesive at least. If you use boards then an airtight but vapour open membrane is an option, but Diathonite acts as an airtight layer.

Ecological Building Systems have IWI documentation for the Lime Green Warm Shell wood IWI and also sell Diathonite Thermactive (which is more insulating than the wood), they will do the thermal calculations for you too.

Basically going this way, you are looking at no vapour barrier but the bottom of the wall will need treating to keep the damp out. Diathonite actually do a bunch of options, including some for walls affected by salts. Details are a bit lacking but case study of a damp cottage treated with Diathonite IWI: https://www.ecologicalbuildingsystems.com/document/download/504

Planning for treatment around any windows to avoid cold bridges is needed too.

It is quite a number of different products layered together but relatively simple/familiar for lime specialists to apply (and quote for).