However, the security of Bitcoin against a 51% attack depends on the value of the mining revenue. If the value of the fees are low, then the security will be low. The real question to answer is then, how low is too low?
If security will be low, 51% attacks would be cheaper to execute, and as the result all users will require more confirmations for transactions. If right now 1-3 confirmations are sufficient for nearly all uses, in this theoretical future with low security 10+ transactions would be the standard. that's ~2 hour wait, which can be pretty bad for some uses, but if by that time LN would be widely adopted, it shouldn't be too big of a problem. So, maybe Bitcoin could guarantee enough security for most purposes with transaction fees alone.