Bitcoin Core limits the amount of memory dedicated to the mempool data structure to 300 MiB by default. When this memory limit is reached, your node will start evicting transactions with the lowest descendant feerate (a heuristic for what’s going to be mined last), and then increase its minimum feerate to the feerate of the last evicted transaction + 1×incrementalRelayTxFee. If “too many transactions get submitted”, there still will only be one block full of transactions added to the blockchain every block. More competition for blockspace means that the minimum feerate in the block is pushed up. Higher feerates means that the subjective value of transactions must be higher for the senders to bid sufficient fees for the transaction to get into the block. That’s bad news for transactions whose subjective value is low. I’ll leave it up to you to categorize whether that would apply to LN transactions or not.

Accepting transactions below 1 s/vB means that it cheaper transactions can be used to fill up the mempool. It makes the price discovery for blockspace more finegrained, but doesn’t fundamentally change the mechanism to reach the equilibrium. If there is low blockspace demand, there might be a few more transactions added to the blockchain that otherwise would not have occurred. It also makes consolidation of a lot of the UTXOs created in the past two years much more financially viable.