A lath plaster ceiling can be repaired. If the laths are in good condition, a lath and plaster specialist can re-plaster the existing laths. If there are underlying issues of damp, rot or woodworm in the timber, then some or all of the joists and laths will need to be replaced. Suspected damp should be investigated with a damp & timber survey. In severe cases, you may have to replace beams, in which case a structural engineer should be consulted.