Looking at TripAdvisor, and taking your requirements into account, the Thorold Arms at Harmston might meet your needs:
http://www.tripadvisor.co.uk/Restaurant_Review-g186336-d2564000-Reviews-Thorold_Arms-Lincoln_Lincolnshire_England.html
It's just south of Lincoln and should be easy to find.
Since there are recent reviews, it's clearly still in business but their website seems have been hacked as their domain name is now being used by a (probably dodgy) overseas trader advertising trainers! So a phone call to the pub (01522 720358 ) might be a good idea, with a request that the landlord posts (or emails) a menu to you.
There are further possibilities amongst the listing here
http://www.tripadvisor.co.uk/Restaurants-g186336-Lincoln_Lincolnshire_England.html
However you should note that the Hume Arms, at South Kyme, is (despite its post code) nowhere near to Lincoln and possibly hard for people to access. The Duke William, in Lincoln, is currently closed for refurbishment.