Which improvements could feasibly be made to Crewe – Newark (/ eventually Lincoln) and Norwich – Liverpool services? I think the starting point would be to have all of the latter services have at least four carriages. Some already are from what I can tell from Real Time Trains, so I don't think infrastructure would be an issue; just finding rolling stock.I don't think either service needs to be more than hourly*, but almost all of them being two carriages feels rather unambitious.
*Apart from maybe between Derby and Stoke-on-Trent, the only section without any other services, even if changing at Tamworth can work out quicker for Derby to Crewe.
Between Derby and Crewe, I think ideally there'd be a second hourly service, but I don't know if either Stoke, Derby or anywhere nearby has the capacity for terminating such a service. There's little enough demand from the intermediate stations to stations east of Nottingham (~1 person per day from Uttoxeter and Tutbury & Hatton combined to Newark) that I don't think both services would have to be stoppers between Derby and Stoke-on-Trent. I'm also not sure if any time savings would justify skipping stations, even though Brampton and Bardon Mill, for example, only get 1tp2h off-peak when there's 2tph on that part of the Tyne Valley line.