I think it's clear Lincoln needs big improvements in it's services, both to regional and national destinations. A few ideas:
1tph London KX (EC) via Newark NG
1tp2h Cleethorpes (EC) calling Grimsby only
1tph Swansea (XC) via Nottingham, Derby, Birmingham & Lydney
1tph Cleethorpes (XC) calling Market Rasen & Grimsby only
1tph Liverpool Lime St (TPE) calling Retford, Worksop, Sheffield, Stockport, Piccadilly, Oxford Road, Deansgate, Irlam, Birchwood, Warrington Cent, Widnes, Liverpool SP, Liverpool LS
1tph Leeds (NT) via Doncaster & Wakefield Wgate
1tph Sheffield (NT) calling Gainsborough, Retford, Worksop only
1tph Sheffield (NT) all stops
1tph Birmingham NS (EMT) via Leicester, calling Newark Castle, Nottingham, Beeston, Loughborough, Leicester, Hinckley, Coleshill Pway
1tph Skegness (EMT) via Sleaford & Boston
1tph Peterborough (EMT) via Spalding
1tph Cleethorpes (EMT) via Market Rasen, all stops
1tph Nottingham (EMT) all stops