If the Bitcoin market goes down then mining will stop altogether.
I disagree. The difficulty will simply drop low enough for few miner able to continue mining at profit. Besides, i expect some Bitcoin enthusiast will start/continue mining to keep the network alive.
I think you're overestimating LN as scaling solution. People who rarely make transaction (usually investor and holder) wouldn't bother use LN, unless they're willing to "lock" their Bitcoin on LN channel.
Possibly, or more people are going to keep their funds in their own wallets and then put them into massive LN routing services and use their wallets. Knowing they are not secure but neither is the cash in your wallet. So you keep your cold funds cold and your hot funds in a very insecure way, but not enough to matter.
The idea of LN routing service is interesting. But looking at current condition where routing fee is very low, IMO it's not attractive enough for many people.