Lincolnshires major problem was a combination of cutbacks and Central Trains how ran the service for operational convenience rather than provide a service the passengers wanted to use.
BR killed of before privatisation the direct service to London, you can sort of understand why it was never as well used as Hull or Inverness (the other places that get one train per day). BR also killed off most trains after 8pm. The drawing up of the Franchise map wasn't kind either, a lots of trains stabled in the Cleethorpes area now they must return to Lincoln empty. so the 0556 runs ECS, and the 0700 Grimsby - Newark runs in service at a time when no-one wants to travel. Under BR it would have been the units first run of the day and it would have got to Cleethorpes by running a later service in the evening. Before privatisation there was a service at 21:15 & 22:20, the stock stayed at Cleethorpes to run early morning services. The 21:15 was very well used but now the cost base must include the ECS to Lincoln. Cleethorpes - Sheffield was virtually killed at the same time, but it could see many more passengers with decent connections at Retford for the ECML.
In the early 1990's the 153 was introduced and resulted in serious overcrowding on the Grimsby - Newark and Lincoln - Nottingham routes, how did BR tackle that problem, make the service less desirable and encourage people from Grimsby - Nottingham / Birmingham to travel via Birmingham. The legacy of the 153 is still a lot of overcrowding.
Looking at each line in order.
Lincoln - Sheffield
This line has in fact improved in terms of frequency, it was only every other hour under BR. But it is very slow at 90 minutes between the two towns stopping at many local stations between Worksop and Sheffield. Pacers don't help either. To be honest however I can't see how apart from getting rid of the pacers how this line can be improved much. I don't think it will ever be justified to run Lincoln, Saxilby, Gainsborough, Retford, Worksop, Sheffield. But maybe if the service was sped up more passengers would use it.
Lincoln - Doncaster.
This is a line where you think why do they bother? 5 trains per day and 2 of them after 6pm. Want to get to Doncaster before 10am for work maybe? forget it. Likewise the first arrival at Lincoln after 11am not much good for people wanting to use it for a business meeting. Some of the connections are dreadful, take for example the connection of the 13:55 Aberdeen - London service, arrives at Doncaster at 2028, unit leaves for Lincoln at 2033, Doncaster is a 7 minute connection, at that time of night would it really make much difference in terms of staffing and network congestions to depart at 2038? I doubt it but it would make it a more useful connection. Leeds services are better for connection but that is more due to the improvements in frequency on the mainline. BR used to run the line all day. An earlier start would be a big plus for this line and improving the connections to Scotland. The problem here is the 153 used to operate the service is needed for peak hour strengthening of the Sleaford line! A lot less service run though to Peterborough than under BR denying Sleaford and Spalding connections north and Gainsborough connections South.
Peterborough - Lincoln
This line is OK off peak but again with the single shift between Sleaford and Spalding totally useless for commuting or travel to London! Hopefully once the upgrade is done this line will be able to run for longer but you can't get to Peterborough from Lincoln before 930 currently and must leave at 1620, going the other way you can't arrive in Lincoln before 1000 and the last train is 1600. Passengers from Methringham and Ruskington would love to be able to use the train to get to London for a day trip with one change at Peterborough but they can't. Running Lincoln - Peterborough all day would make no difference to staff or rolling stock of the TOC as Lincoln - Sleaford and Spalding - Peterborough does run most of the day.
Lincoln - Nottingham.
The government has ruined this line by forcing CT to stop running to Birmingham in order to fudge the PPM's the flow was very strong it is more important to have a 90% PPM then run trains to where passengers want to go. Not it is a very slow Lincoln - Leicester service stopping at places like Syston which very few people from Lincolnshire wants to visit, certainly a lot less than the places we have lost. To make matters worse trains from Birmingham still run late so you miss connections so the average journey time has increased. Even between Lincoln and Nottingham the service is too slow with most trains stopping at every stations upto EMT taking over. Less stop at small places now BUT the service was not sped up. It still takes about 1 hour, the A46 is getting duelled so more people will be hitting the road once it is complete unless this route is improved. In the perfect world give it to XC and run it Birmingham - Derby - Nottingham - Lincoln calling at Newark Castle only. Serve the local stations with a 153 shuttle even if this is only between Newark and Nottingham to avoid the flat crossing. I recall an article in Modern Railways saying this could be done with the same resources as now even if the shuttle ran all the way to Nottingham.
Grimsby - Newark.
Main problem here is frequency, some of the connections at Newark are poor but some are also very good. If you living in Market Rasen an work in Lincoln you can arrive at Lincoln at either 0800 or 1024, hardly going to get people out the car, going home it 1500, 1718 & 1950 so really on the 1718 any use for most people. Connections onward to Nottingham are not good at times and commuting to Grimsby is not the best. Hopefully when the East Coasts Lincoln - London service is introduce the Grimsby - Newark will be change to Grimsby - Nottingham with a good connection for London at Lincoln. If every service connected well that would be a drastic improvement on what exists now. The 153's often can't cope either.
Skegness - Nottingham.
The frequency is OK, the speed is low but so are the competing roads, it suffers in the summer from lack of carriages on the trains. The main improvement here would be to improve connections at Sleaford for Lincoln and Peterborough. I am sure returning it as a direct service to Derby would also be welcomes.
A lot of improvements can be made in Lincolnshire just by making sure the connections work, the trains run at useful times. However it is a double edge sword, if passengers numbers increase the overcrowding to the 153's would be awful so in some ways it is not in the operators interest to encourage people to use the services.
Once the Lincoln - Peterborough upgrade is complete maybe it would be worth running the Lincoln - London service this way. It could do London, Peterborough, Spalding, Sleaford and Lincoln. I am sure Spalding would gain a lot out of this, but Sleaford could be used to provide a faster overall service than going via Grantham. It is 56 miles between Lincoln and Peterborough once the joint line is upgraded to 75mph running it should be possible to do this journey in about 1 hour, via Newark it will take about 55 minutes. So via Spalding it will be slightly slower but the benefit to Sleaford and Spalding will outwiegh the longer journey time to Lincoln. on the ECML Grantham will still have lots of choice with HT and NXEC. Newark may lose out a little but the solution is simple, let Grand Central stop there!