Most of the ceilings in my house are lathe and plaster, we bought another house in 2010 and have been gradually restoring it, I took down two of these types of ceiling and it is utterly filthy work. Part of the original ceiling had been boarded over with plaster board just to make it more interesting and hard to remove. A truly mucky job - the dust gets everywhere!
As for staying up the thick stodgy lime mortar/plaster is bound together in some case with horse hair, it is then layered on quite thickly forcing between the narrow wooden lathes, the material sort of squelches behind the wooden strips and once dry holds the whole lot up! They tend to be quite thick for this reason typically 2-2.5".