The main motorway structure in the UK is a letter H with regional additions and a letter A in Scotland. The Lincolnshire motorways would follow on from this arrangement.
Whilst proponents for an east coast motorway sometimes envisage the retention of tolls on the Humber Bridge, and thus increased traffic to pay it off, this is quite cynical. My view is that the east coast motorways (Lincolnshire and Norfolk) are needed on their own terms, and that only if the Humber Bridge is without tolls will the national road network extend to this side of England because with tolls (even with the past one-time reduction) the traffic will avoid new routes and they will lose their potential in the same way as the Humber Bridge.
The desperately needed M17 roughly follows the path of the A17 and the A47, linking Norwich to Nottingham M1 (north) and giving via a southern spur access to the A42/ M42 to Birmingham and the South West access as well as the A50 to near Derby and across to the M6. This gives fast access into Norfolk from the Midlands and North. Including both western-end spurs, it is a three lane each way motorway except east of Kings Lynn, and the A17 to Norwich is dualled. The present A11, A14 arrangement is too far south; the north Midlands and the North need their own penetrating motorway.
The descriptions below are from south to north.
There should be two north-south Lincolnshire motorways/ motorway standard dual carriageways.
The M15 is Lincoln's access from the M17. It also improves the existing eastern bypass from the A46 Foss Way. The A15 is necessarily dualled from Lincoln to near Scunthorpe (long required). It connects into the M180, renamed as M15, and receives the M16/ A16 going north.
The principal Motorway is the East of England Motorway M16, and east is where it should go. It starts with the existing Peterborough A605 southern bypass renamed to the A16 where traffic can easily come from the A1(M). The motorway northward goes straight to three lanes each way. It merges with the M17 until it connects with a route easterly for the resorts of the county of Lincolnshire to facilitate travel towards Grimsby, with two lanes each way. But it curves in for a complex merger with the A180 and M15 to use the existing A15 dual carriageway north as now the A16. The A16 crosses the Humber Bridge and merges into the A63/ A16. The motorway is re-established with two lanes each way at the M62 to go up to a dualled old A1079 now A16 until a motorway section connects via a spur with the York bypass and gets to the old A19 south of Easington. This now A16 is also dualled north and a complex junction east of Thirsk with the already principal A19 for Middlesbrough takes the M16 via a three lane each way motorway across to the A1(M).
The M11 is extended with a junction at the A142 from the A14 north, connecting with the M17 north of the Wisbech bypass. In effect it talkes the M11 up to near Kings Lynn.