2nd layer scaling solutions are inherently vulnerable to centralization
It is important to have the same definitions in mind when discussing things like centralization. In Bitcoin, decentralization means censorship-resistance (due to many parties involved that take random turns producing the blocks), impossibility to do any action to bring down the whole network (in centralized systems, this would be chopping off the head), and custodial decentralization (no need to trust someone that they won't steal your funds, because they can't). You would have the same in LN: censorship-resistance (if 10 routes don't want to do business with you, you route through 11th), can't bring down the whole network (you bring down big hubs, and the little ones take their place), and custodial decentralization (you still don't trust anybody other than the math, hubs are not custodians of your funds). What's left is perceived centralization, however, cause such a network would tend to center around hubs with the biggest liquidity and connections, so it would look like hub-and-spoke topology.
It's a bit offtopic here though.
because of having a parallel block just doesn't sound very different than suggesting an increased block size
Very different. One is a hard fork resulting in a network split, the other one is a soft fork, not affecting legacy software in the slightest. That's the whole point.