The purpose of plaster is to make the surface look nice - it scarcely offers any insulation value at all.
Single skin walls between dwellings are unusual. You really need to get to the bottom of where this dampness comes from - just covering it over is likely to lead to further problems every time. What has the neighbour got on the other side - a shower?
Assuming you try but you really can't prevent the damp wall, the way I'd do it would be to seal off the damp getting through by covering it 1000 gauge damp proof membrane (plastic sheet), batten it over to hold the plastic in place by using 25x38 vertical battens spaced at about 600mm apart, then nail plasterboard over that. Then you could skim the surface to get a smooth finish.
No, you can't claim on your insurance - you might be able to claim on next-door's if the damage is being caused by him.