Most of the roads are like rough MTB trails, and that from somebody who raced cross and mtb for many years. There is a little bit in Willingham woods but not much. Loads off of road riding around farmers fields, but be prepared for a lot of pushing.
What part of Lincolnshire are you looking at, it is a very large county. Take Boston for instance, I admire any cyclist who can start any decent lenght ride with 7 miles on a straight road where the kerb is the highest point, not that many of them have kerbs.
Now for something positive, the wind can be good when it is on your back, seldom is though.
We don't do a whole lot of MTB riding in terms of Sherwood type trails, but do have some good rides on the Wolds by piecing together Bridleways etc.
If you are going to be near to Market Rasen, then Rasen riders have an MTB trail at Walesby (I think) which is only available to members, there are more details on their website,, afraid we cant help more than that, we have never ridden with them.