You actually have to be able to say: "See, I found a route A-D through B and C: ABCD and all nodes are sufficiently funded to execute the payment."
And that's the big unsolved issue. Can you make an algorithm that will reliably do the latter while keeping the network decentralized?
I think this is very hard, as the channel states between individual nodes will change for each payment, and that's entropy that somehow needs to be synchronized.
Of course, simple centralized solutions like making B and C big enough ("banks") to deal succesfully with almost any payment are possible.
But solving this problem is pretty damn hard, and I have yet to see a satisfying solution to this. Note that satisfying absolutely must include being decentralized.
Because else, we can as well do the simple and sane thing and scale just on-chain, which also ensures that the miners get their fair share of the pie and makes it less likely that the bottom falls out because there's lots of layers, each taking a cut, to the system.
Now, don't get me wrong: I am fine with LN and I think it might have good use in the micro/nano-payment space. Regular, simple payment channels (like BCH and BTC have since the beginning) might fully cover that use case as well. Who knows. In any case, LN as the (and the only) solution to scaling is not going to work out.
There is a lot of technical complexity to this, and no real working proof at scale (AFAIK there is no production implementation even at a small scale).
Lightning Network at scale will involve routing problems between coinholders analogous to a mesh network (or more realistically, FidoNet/UUnet) which risks centralization since those problems are not solved at scale in any fashion except hub-and-spoke/backbone. BGP is not an acceptable solution for LN since it involves a substantial degree of trust, and manual routing devolves into centralization.