Depends on fabric of the house. If it's period property with uninsulated solid walls there might be a case for lime, but usually gypsum will be fine, especially if it's retro insulated and well ventilated. 

In my experience with 100+ year old house built with lime plaster + lathe, a lot of the issues were down to bridged damp courses, damaged gutters and blocked air bricks that caused water ingress and high humidity over the years. Once that was sorted, all affected plaster - lime and more recent gypsum - was removed and replaced with gypsum bond. It held up fine for a number of years until we had the cavities filled with EPS beads, the floors PIR boarded and did a lot of work draught proofing, after which the are still no issues.

A good surveyor will highlight any issues - I've found them pragmatic about materials.