I very much doubt the 397s will leave TPE. They are well suited to the Manchester - Scotland route, and there’s just about the right number of them for the job.
If the 397s were to leave TPE, the place I see them going is Lumo. 12x 397s to Lumo would allow a doubling of capacity in the existing paths, and the 803s could move the other way reducing the number of new 80xs TPE would have to order to compensate for the loss of the 397s.
As for LNER, they’re going to have a microfleet of some description regardless what their rolling stock plan is. It makes more sense for them to keep the microfleet they’ve already got than to take the 397s, which would be thoroughly unsuitable for LNER for a variety of reasons.