Does LN require an on-chain "emergency lane" to mitigate systemic risks? According to LN social slides, a fee market (in other word: "congested mempool", to my understanding) is good. But, there's systemic risks around penalty mechanism, so some sort of on-chain scaling (which looks like an emergency lane to my understanding) is still needed to mitigate them.
As far as I understand this is not needed. Let us assume we have an congested mempool and someone publishes an old channel state. This transaction will not be mined directly as the mempool is congested. The timelock during which this transaction can be revoked via the penalty mechanism is a relative one and starts as soon as the transaction is mined. So, this would happen once the fees are down again and then one can use the fees in their breach remedy transaction. 

That being said, on-chain fees are a challenge for lightning. While a collaborative channel close can take the current state of the mempool into consideration and adjust the fees so that the channel closes quickly the case of of a unilateral close is much more difficult. When negotiating a new channel state, we don't know what the fees will be in the future. So, when force closing we might have over or underpaid but we can't change the fees anymore since this would require a signature from the unresponsive party.