I've seen the idea of the Yorkshire & North Eastern half of Northern be merged with LNER posted on here a few times, similar to regional services being incorporated into GWR and EMR and it's actually not a bad idea. Plus it'd be nice having red back on the trains in West Yorkshire, akin to the old Metro Trains.

Just have the NW side rebranded as North Western, retaining the modern livery. Who'd keep the 331s/195s though?
The transpennine routes under Northern (York to Blackpool, Leeds to Manchester Victoria, Leeds to Morecambe/Lancaster/Carlisle) were all operated by Arriva Trains Northern so they can still be kept by LNER. I'd also keep the Leeds to Nottingham train. I'm not sure about the recent long distance services from Leeds to Chester, Wigan and Lincoln though. I'd maybe just have the former two terminate at Victoria and the latter at Sheffield.
I also agree that XC and TPE should merge, or at least give the Liverpool/Manchester to Scotland TPE routes to XC, as they don't cross the pennines. I'd also give the Liverpool to Norwich route to XC as well.