We need massive amounts of settlement tx's on-chain, when people open & close channels on the Lightning Network and the price of a bitcoin must grow exponentially for miners to be profitable. 
With a big user base who is transacting daily on the LN, there will be enough on-chain transactions.
And if not, the fees for the on-chain transactions will be low enough for users to be attracted by on-chain tx's again.
I believe this will find an equilibrium.
The price does only have to grow exponentially if the miner do want to keep increasing the hashrate.
If mining gets unprofitable, the miner with the highest costs and lowest capital will stop mining and vice versa. This should also find an equilibrium.