There are no trains on Sundays directly between Lincoln and Sleaford.
Lincoln - Newark - Grantham - Sleaford is not a permitted route, but would this be allowed on a Sunday?
I don't think so - the railway can't be expected to provide service 24/7. Those fares apply when trains run, and not when they aren't scheduled to run. If you need to make the journey on a sunday you need valid tickets.
Its like turning up at Denton on a sunday and expecting either a taxi, a special train, or a hotel room until the Friday.
Re NRCOC clause 13a ii. Quote:
"The route you are entitled to take
(a) You may travel between the stations shown on the ticket you hold in:
(ii) trains which take the shortest route which can be used by scheduled passenger services"
Note that is is "the shortest route which CAN be used by scheduled passenger services", not "the shortest route WHICH IS used by scheduled passenger services".
One interpretation could be get your quail out, ignore the track that isn't passenger rated (watch those FPL's) and that is your shortest route, whether or not it is actually used by passenger trains or not.
I don't think that is what is intended, so we return to "shortest route actually used by passenger services". No words regular/frequent/daily. If the shortest route is only used once a day then (unless other options are permitted by the RG) this is what you have