Can't advise as to the park and ride but there's a delightful little site at Welton Golf Centre which is by a fishing lake, has electric and facilities in the club itself. Was £8/night when we looked. 01673 861888
Welton Manor Golf Centre
There's a C & CC CS in Brant Broughton which we definitely wouldn't recommend.
Or, about 17 miles from Lincoln, Heath Farm, Rauceby. Electric, loo and hot water. Tel Paula Ireland 01529 488409. £7.50/night
Have fun, Lincoln is lovely
Jan