LNER can’t decline to accept routes Any Permitted tickets issued, regardless of the medium the ticket is issued on.
Oyster fares are defined with 46 different route codes in the fares data, though, although how you are supposed to know that when you travel is anyone's guess! The top four are both flavours of
Any Permitted,
Not London and
London Not Underground, but there are some more exotic options in there too. I do wonder how accurate the data is for these, as there is a
Not Gatwick Express fare to Gatwick, but nothing more permissive, and you can definitely use PAYG on the Gatwick Express for extra £££s. (Of course, GX is not a TOC, but I don't think that matters to the point that the Oyster fare in question could be defined on the
Thameslink and Great Northern flow or whatever to exclude LNER, but it is never quite 'sold' in the way that a normal ticket would be, perhaps that's what makes any LNER exclusion unworkable.)