The Man in Seat 61 is giving bad advice about the East Coast Main Line- on that line and some others it is 24 weeks out, the tickets won't get any cheaper on 29 January.
On the 0930 the best fare is £66.60.
Both before railcard discount.
Yes your travelling colleague qualifies for a Disabled Railcard.
Do not be afraid to book assistance at Kings Cross, Edinburgh and York (if you change there)- https://www.lner.co.uk/our-trains/assisted-travel/
Note also that railcard discount also applies to 1st class- which makes it an affordable splurge- more room, lounge access before and after, and an included meal (breakfast in that case, but you may also get an early lunch with alcohol north of Newcastle).
On the west coast main line into Euston (a bit different from the East Coast) I have a lot of evidence that around 4 weeks out is the actual sweet spot, that is when I generally book.
Today I travelled on a bargain basement Advance Fare which I booked late yesterday evening. It was as cheap as it would have been 12 weeks ago. That is quite normal on my local line.
Equally there are almost always cheap (but not that cheap) advance tickets until 2 minutes before train departure on the ECML.