LNER Website

17th and 18th of November are a Saturday and Sunday. Weekends are typically when they do maintenance, and have to implement temporary one-off timetables. I would guess that is the case here, they haven't yet finalised the work plan, so can't say (yet) which trains will or will not run.

I checked on the National rail site. See here: http://www.nationalrail.co.uk/service_disruptions/currentAndFuture.aspx?TravelDate=17%2F11%2F2018&TOC=gr
Then click on "Amended service between Doncaster and Peterborough on Saturday 17 and Sunday 18 November".
And you get (note the "please check back nearer to the time" at the end):

Start date 17/11/2018
End date 18/11/2018
Route affected
. . . .
LNER between Aberdeen / Inverness / Edinburgh / Newcastle / York / Skipton / Leeds / Hull and London Kings Cross
Description
Engineering work is taking place between Doncaster and Peterborough, closing various lines.
Trains will be diverted via Lincoln Central, extending journey times by up to 60 minutes.
. . . . .
LNER
All day Saturday and until 12:00 on Sunday, a special hourly service will run between Doncaster and London Kings Cross via Lincoln Central.
No trains will run between Newark Northgate and Peterborough. Other services to and from the North will start and terminate at York, Doncaster and Newark Northgate.
Road transport will be provided to run between Newark Northgate, Grantham and Peterborough.
Check before you travel:
These changes are not currently shown in the National Rail Enquiries Journey Planner, please check back nearer to the time of travel.

Ah, Chris - thank you! Unfortunately, maintenance on the weekends makes perfect sense. I appreciate your "next level" of insight.

Edited to ask:

The plan is to go from Edinburgh to York and stop over for a few hours before catching a second train to King's Cross. So if I understand correctly, there will still be some service available, the schedule just isn't confirmed yet. Is this correct? Will we end up on a bus with slower results? I am new to train travel of this kind (train to Windsor, train to Gatwick are my only references) and am not feeling confident about how to interpret this for planning. How far out do they usually have the amended schedules set?

Thank you

MNFerst, There will be trains
The blockage is south of York, between York and London. If you look at the page I posted, there is a link to a map here: http://www.nationalrail.co.uk/static/documents/maps/DoncasterPeterboroughNovember.pdf

It helps to know a bit of local geography. The blockage is between Doncaster and Peterborough. It says "special hourly service will run between Doncaster and London Kings Cross via Lincoln Central.". That diversion route is not electrified, so they can't use their normal (electric) trains on it. They will be running a shuttle service of borrowed diesel trains on the slower route via Lincoln, with the electrics just running north of Doncaster. The buses are just for people wanting to get between stations on the normal route.
Edinburgh to York will be the normal route.
York to London you will have to change at Doncaster, and it will take longer.

But, as they don't yet know how long the blockage will last, they can't publish a timetable yet.
You just have to wait and keep looking. The good news is nobody else can book seats either!
Or stay overnight in York, and travel south on the Monday morning (19th)

I like Chris F's last sentence above. Traveling during times of disruption is absolutely never fun. You can expect reserved seats to go out the window (not exactly literally), the replacement train may or may not have as many seats as the normal train, and adding an hour for a diversion is not always fun.

Nothing wrong with Lincoln, mind. Spectacular cathedral, pretty nifty castle, a very steep street (called the Steep Street). But that's not why you are there (at least not on this trip).

Do you have enough air in your schedule to go up to London on Monday?

Big thank you to Chris F and Nigel - we are going to extend York to an overnight stop and move into London on Monday.

Your patient advice is very much appreciated!