In my opinion, LN is "only" a part of the scalability puzzle, but a pretty big one. LN can rise the Bitcoin capacity
safely by 1000x or more, without any fundamental disadvantages for small-to-medium transactions.
But I write
safely for a reason, because if LN adoption becomes too high, a point could be reached where attacks could have a success probability of higher than 1, because the closure of all affected channels by the attacker would take longer than the timelocks expiration. This point would be reached earlier if the network becomes relatively centralized (hub-and-spoke model), and later if there are lots of well-connected hubs.
What we must aim for, thus, is to not let grow the biggest LN nodes too much - ideally there should be lots of medium hubs of a few thousand channels each. This is of course currently not an issue, as the whole LN has only
about 50.000 channels, which could all be closed in 2 hours given the current blockchain capacity. But once there are nodes with more than 100K channels each, things could become more critical, as if a 100K node decides to try out an attack, the closure transactions would compete with regular transactions, and if the blockchain is quite full, then it may take several days to close them and consume lots of transaction fees.
Anyway, I think we are far away from that situation. The other parts of the puzzle may be:
1) altcoins/alternative blockchains - let's face it, they will always exist, and if there are a few strong ones of them, it's better for the resilience of the cryptocurrency ecosystem as a whole, because not everything would be concentrated on a single blockchain. But I'm also quite sure that no (decentralized) altcoin will be able to scale
fundamentally better than BTC, all "big block" and "zero fees" models come with tradeoffs.
2) pegged BTC coins on alt chains, either centralized (wBTC) or fairly decentralized (BitBTC)
3) maybe pegged sidechains - I had big hopes on that in the past, but I'm not so sure it will ever get massively adopted, as for example the
Drivechain project is taking longer than I expected, but there may be a surprise breakthrough.
4) centralized solutions, like Bitcoin debit cards, which will be ok for smaller transactions in many cases.
So I believe the scalability problem will probably be solved fully, but without LN it would be difficult. I also don't think that fiat money will disappear, so Bitcoin will not need to have a capacity for
all monetary transactions which are made in the world.