I have seen pictures of Sambhar lake and it looks like a place where I would like to take my own tent and spend a night or two so I was wondering if this is allowed at Sambhar lake. I searched a lot but there is no such information anywhere.
There are no notices posted any where at Sambhar lake that you can or cannot pitch tents there. There is no police or authority present at Sambhar lake to prevent you from doing that either.
Legally speaking it is government land and is part of a wild life reserve and you are not allowed to pitch tents there.
My advise to you would be to pitch your tents near the Sambhari devi temple where there is a small shop as well and a few people live there including the priest and his family so just talk to them and let them know what you intend to do. Sambhri temple also has a small parking area where they may allow you to pitch your tent as that is where I parked through the night as "Neel gai" roam on the lake bed even at night besides some other animals.