There appears to be a couple of nice campsites at Kirkby on Bain, which has a very nice pub called the Ebrington Arms. This is near Woodhall Spa.
Or the 13th century, Blue Bell Inn, at Tattershall Thorpe, next to Coningsby, also has nearby camping. Possibly the oldest pub in the county.
Also, the Coach and Horses, at Hemingby has its own camping on site.
And finally, the Durham Ox, at Thimbleby, has a camping field onsite.
I will make a few further enquires, as my prefferred option would be the Blue Bell Inn, but I will phone them to get more info.