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 (especially as they are) the traffic will avoid new routes and they will lose their potential in the same way as the Humber Bridge.
The M17 roughly follows the path of the A17 and the A47, linking Norwich to Nottingham M1 (north) and giving access (south) through to the Derby link and A50 across to the M6. This gives fast access into Norfolk traffic from the Midlands and North.
There are two north-south Lincolnshire motorways/ motorway standard dual carriageways. The M16 route starts in the south at the A1(m) with the existing Peterborough A605 southern bypass renamed to the A16. It continues north as the M16 until reaching the M17, whose route it shares until branching off to form a west of Boston route (it works out not to share and dual the railway origin road that is the A16 now because of the way eastward travelling traffic would branch on to this road - the alternative is junctions to the A52 via Hubberts Bridge). The M16 opens up eastern Lincolnshire and its resorts and market towns, but is an alternative route north for national traffic.
The M15 links Lincoln to Scunthorpe with a much improved road and into the national and regional motorway network. Although there is a kink to the Lincoln bypass and back along the existing M180, it offers a more direct route to those who who wish to travel to West Yorkshire, Manchester and the North West.
The northern end of this motorway system could be called either the M19, M16 or M15. If it is the M19 it then localises itself whereas the idea is it links to the south as one eastern route. It would also require the road that is the A19 south of York renumbering. There is a psychology of increasing choice to call it the M15, but the M16 route is the most efficient and continuous alternative north-south route in the east. Nevertheless there is still a need to improve the Lincoln to Scunthorpe route and link it in with the motorway network, and so it becomes the M15, with an A46 spur that goes to the A1 but the M15 continues through for easterly and alternative southerly traffic. So the M180 would be renamed the M15 on the westerly side of changes and meet the renamed A16 on the east, which goes into the M16 going south. The Humber Bridge and link road would be renamed to the A16 and the A63 would share with the A16 before the M16 resumes north.
The route should shadow the A1034 on its western side going north west, before sharing and renaming the A1079. It can then resume to cut a corner whilst staying connected to the York outer ring road system and continue corner cutting and renaming its part of the A19 to the A16 before as a motorway cutting across to the A1. It is possible, however, for the A19 to Teeside to be renamed the A16, although the A19 is a large national and regional road in its own right, thus freeing the number 16 to go to the A1. This also means that the M16/ A16 route runs from the A1 to the A1 and provides an alternative north south route for when the A1 is very congested, although as a totality it involves extra mileage in its eastward swing.
The northern M16 should be three lanes (and hard shoulder, as with all motorways and many new dual carriageway A roads) in each direction due to the traffic from Hull. This should also include A road sections. The section of the M16 in Lincolnshire from the A180 to north of Spalding needs only have two lanes in each direction. The M17 should be three lanes in each direction (plus hard shoulder). The M15 should be three lanes in each direction between Scunthorpe and Lincoln and two lanes each side south of Lincoln, although the M16 spur to Peterborough should be three lanes.