Hi Sharon -
As I understand it Lumo are cheaper, no frills, no ticket options, but LNER have more options on frequency. Travel time is roughly the same and both depart London from Kings Cross.
That said, if you decide to travel LNER then the most economic way to do it is to book ‘Advance’ tickets which does tie you to a specific train (changing trains is not an option without purchasing new tickets at great expense unless there’s some problem with LNER - we once returned to London from abroad when bad weather had disrupted the timetable and having checked with staff we were waved onto the first available train given that the one we were tied to wasn’t running).
Advance tickets are in the main released about twelve weeks out from date of departure, but keep an eye on the LNER website to see if they are released any earlier - pandemic has suppressed rail travel so they might be keen to fill seats early.
And, where it is an option, ALWAYS reserve seats. It costs nothing to do this and is part of the booking process - getting three seats together if travel is returned to normal by June on a mainline train is next to impossible.
If you plan to travel extensively by train then getting a railcard (generally saves around 30% on tickets purchases) will probably save you money in that cost of purchase will be more than offset by tickets purchased). There are several types of railcard - do the research to determine which one is suitable. As far as I am aware you can use your railcard on all types of rail journey on the national network.
Have a great trip - it’s really not as daunting as it sounds!
Ian