After a little shopping I returned to the station to come home, and found that my reserved seat was on one of the aforesaid local Lincoln-bound trains as far as Doncaster, where I changed and boarded my East Coast service for Peterborough, enjoying the afternoon tea on the way, changing again at Peterborough for Stamford and arriving home on time. My booked train from Doncaster to Peterborough had actually been cancelled owing to some problem with the train, but those of us with tickets for that train were put on the next one which was just a few minutes later and still made the connection with the Stamford train - and fortunately had enough seats, too. And enough tea and cake!
With a Senior (or any other) Railcard and advance booking, such exploration can be very reasonably priced, and it is quite cheap to put together a simple tour visiting a few towns and staying overnight in B&B in some of them. We’ve done it in Scotland: perhaps we should do it closer to home, too!