For some reason, camping doesn’t seem to be very popular in the Lunigiana. The only commercial campsite worthy of mention is the one at Villafranca (Camping il Castagneto).
As in the UK, camping on private land requires the permission of the landowner. Camping on public land located in urban/residential areas is best avoided and usually requires permission from the local Comune. It’s also advisable to keep away from parking areas, roads, tracks and obvious footpaths.
Wild camping in Zone 1 (also known as Zone A) of the National Park is absolutely forbidden on environmental grounds. You can however bivouac/camp overnight in Zones 2 & 3 (B & C) provided that you pitch your tent at dusk, take it down at dawn the following day, stay no more than one night, move around quietly, refrain from lighting fires, leave no rubbish and use a trowel to bury your excreta. Just so you know, the fine imposed by the Forestry Police for unauthorised camping is €100 and that for lighting fires is €2064(!).
Do remember that water is hard to find in the mountains during the summer months so to be on the safe side you need to take plenty with you.
I always take my tent when heading to a mountain hut for an overnight stay just in case when I get there it’s already occupied. To keep weight down the tent I use is designed to be supported by my walking poles.