Keep in mind that Lightning will always need to touch the main chain. Opening new channels for more efficient routes, rebalancing liquidity, withdrawing funds to cold storage, etc. If Lightning is popular but on-chain txs are cheap, channel operators will take advantage of this.

Also there are some advantages on-chain offers that Lightning cannot replicate. On-chain represents the highest form of security where funds can be stored offline indefinitely. Whereas Lightning and other L2s require hot wallets or counterparty risk.