Abellio East Midlands Railway have a dedicated webpage with advice for passengers intending to travel to the market:
https://www.eastmidlandsrailway.co.uk/lincoln-christmas-market
When returning from the market, due to a queuing system being in place, passengers are advised to be at Lincoln Central station 30 minutes prior to the booked departure of your intended return train. Return trains from Lincoln to Grimsby are:
Friday 6th December 2019
17:22 (3 coaches)
20:02 (2 coaches - runs through to Cleethorpes)
Saturday 7th December 2019
16:49 (3 coaches - runs through to Cleethorpes) - this train is expected to be extremely busy
17:22 (3 coaches - runs through to Cleethorpes)
18:36 (3 coaches - runs through to Cleethorpes) - this train is expected to be extremely busy
The revised Cleethorpes - Newark timetable for Saturday 7th December 2019 is available at:
Stagecoach will be running additional buses on services 7 and 8 between Lincoln Central Bus Station Stand D, which is opposite the railway station and the cathedral, close to the market.
There will be buses every 10 minutes for the bulk of the event. Applicable fares:
Adult single: £1.50 (£1.00 after 18:00 on Thursday 5th and Friday 6th December 2019)
Adult return: £2.70
Child single: 75p
Child return: £1.35
Plus Bus tickets are also valid, these are priced at:
Adult: £3.20
Child: £1.60
Railcard holder: £2.10
Note that for railcard holders this is cheaper than the bus day return fare.