Easyjet that day have 5 flights to Gatwick, 3 to Luton, 2 to Stansted, Ryanair have 3 flights to Stansted, and there are probably others.
BA flights are very expensive on this route, to Heathrow, Gatwick and London City.
I would also look into flying from Glasgow- BA flights are usually far cheaper from GLA than EDI (edited- this time EDI flights are cheaper than GLA!- with the best fares, also unusually, to LCY which is easy access to the DLR into London- 20 minutes into Bank station)
Lumo trains are not involved in the strike- they are currently showing one train that day, and have predictably put their prices way up to £75 each.
This is ASLEF (the drivers), not RMT.
The word is that this may be more disruptive than a RMT strike day- and if you wait until train timetables are confirmed between 4 and 7 days beforehand you may find the flights sold out.
So I think I would look at one of the above flights.