If York is a separate region rather than part of a monolithic North England, then why couldn't all of Lincolnshire be part of Greater York instead of merely the Humberside? Or alternatively, why would it be a bad fit to be attached to East Anglia?
Well Yorkshire has one of the strongest regional identities in England. If the county ever became an independent state then we can be sure that its first act would be to invade its neighbours in order to reclaim its lost territories.
Anyway, its really just the south bank of the Humber that has any links with Yorkshire (and even then I suspect the pairing would be resented were there regional governments). The rest of Lincolnshire might not be Midlands, but it does at least have links to it. Pairing Lincolnshire with East Anglia has never been done because East Anglia has often been linked by central government planners with the eastern Home Counties (as is the case with the current East of England region). Were England to get regional government of some kind, a decent case would actually exist for having Lincolnshire (the whole of it) be its own region. It may be
just about large enough...