Of course it is fair to assume that people who wish to travel to London will not actually live on the train station, so whether you go to the airport or the train you have to travel there, and as the airport in Carlisle is not so far away and you are as likely to be able to get to either the train or airport in Carlisle in much the same time then that part of the journey can be ignored.
A quick look at national rail reveals It takes c.4 hours to travel Carlisle to London on the train. Let's assume you have to arrive 15 mins before hand, which is reasonable.
Again, you are unlikely to be visiting Euston so whether you travel to your final destination from Euston or Liverpool Street is largely irrelevant, both have excellent links to the centre of London, and arguably Liverpool street is better from a business point of view.
So, time analysis:
Train: 4hr:15 mins from arriving at the train station to arriving at a London terminus.
Air: 30 min check in, 1 hour flight, no baggage (business travellers which seem to be the aim of the game rarely check in a bag), 15 min transfer to the train (generous at SEN) and 50 mins on the train.
Total time from airport to london terminus: 2hr35 mins
Take the 7:02 train from Carlisle arrive in London at 11:05 (or 11:34 if you take the direct train - go figure)
Take the 07:00 flight from Carlisle and arrive in Liverpool Street 09:10
I know what I'd rather do, probably cheaper to fly as well, and of course if you happen to not be going to central london but somewhere east ….
As a further point, Newcastle to London on the train takes only 3 hours and yet they support (very well) 6 daily flights with British Airways to LHR and a double daily easyJet to Gatwick.
My point is, exactly why is service CAX-SEN such a bad idea? I would say you would certainly fill 2-3 a day on a 72 seat aircraft, easily and likely with a healthy yield ...