The answer is simple, Blockstream will apply SegWit and LN to another Alt coin like LiteCoin and it will function as a true Peer-to-Peer digital payment system, and Bitcoin will loose users to whatever Alt coin that incorporated this. So you will have a 3rd division in this community.
Bitcoin will then serve as a store of value for the hoarders, until it lose enough value that they too will also abandon it. Miners cannot survive in a scenario where mass hoarding takes place. No tx's = No mining, and NO mining = NO Bitcoin.
Actually this thought was also on my mind, though in less radical version -
maybe Litecoin implementing SW+LN will become a go to currency when it comes to actual buying and selling things, however as Litecoin network is not (at least yet) secure enough the coins won't stay there for long and going back to Bitcoin ie. at the end of every day or end of the week - similar to what small businesses do with cash every day or every week - they take it and deposit it to a "safer" place such as bank.
Essentially it might in the end look like this:
BTC hoarder has 8 BTC in his account - that's his monthly salary. He knows every month it costs him ~5 BTC to pay rent, groceries and others so he exchanges 5 BTC to 500 LTC on let's say 7th of the month and slowly using it throughout the month spending the 500 LTC, saving 3 BTC and pocketing another 8 BTC the next month. This is probably similar to what some people do every now and then when withdrawing cash from ATM.
Businesses offering goods and services will be collecting the above mentioned 500 LTC throughout the month as they are selling their services and let's say every week to hedge the risk they might exchange it to BTC and later pay the employees with BTC (as it's not super time intensive).
But then it comes back to what you originally proposed - even though LTC might be less secure in overall, are people going to bother themselves to exchange it twice? Why not just stay on the LTC?
I never really fully understood why there was so much resistance to 2MB block or 8 MB block or other blocks (the technical constrain I don't really buy - storage as well as bandwidth is cheap and if it goes faster than Moore's law then the storage technology will followup), now there is resistance towards SegWit and eventually LN.
Do the miners actually understand that if some 2nd or 3rd most popular crypto pickups this technology then BTC will put itself at serious disadvantage? Only then we can expect overnight switch in sentiment?Full disclosure: I know very little about LTC and I don't own any, just as it's probably 2nd or 3rd most popular crypto I thought to put it here as an example.