Transaction fees are currently 11% of the mining reward, which isn't nothing. If the non-transaction mining reward went away tomorrow, you'd expect the mining

Transaction fees are currently 11% of the mining reward, which isn't nothing. If the non-transaction mining reward went away tomorrow, you'd expect the mining power to decrease 10-fold, and the work securing the Bitcoin network to be about $700M / year. By itself, I'd say $1B / year might be enough security. Any malicious nation-state wanting to attack the network through mining power would need to spend on the order of a billion dollars, which is a lot even for a large government. On the other hand, if you did have a sharp discontinuity, and not a gradual turn-down in spare capacity over many years as the mining reward gradually decreases, you would have a unique opportunity for attackers: a huge amount of mining equipment would likely be dumped on the market at once, and an attacker might be able to build up their own capacity quickly and cheaply. The Lightning Network helps with scaling the number of transactions, but it doesn't change the need for an adequate amount of work to be done to secure the core network; you still need to spend a large number of dollars (or Bitcoins, if you prefer) each year mining, so that attackers cannot afford to attack the network through that venue. The Lightning Network gives you a larger tax base for this security tax to be levied on, but it doesn't change the fact that when you ask the question "How much money should we spend mining Bitcoin?" the only secure answer is "As much as we possibly can.".