The scenario is as follows:
You have a payment channel open. Someone attempts to defraud you by publishing an older signed tx (that since has an update). You have N blocks to get your updated transaction in, which will claim all of the funds of the channel, otherwise the old TX is spendable. However, due to congestion/high fees, it is not practical to submit your dispute transaction. In addition, the fee is included in the updated transaction, and it may be insufficient to get into any block.
Example: You have a 1BTC bi-directional channel with another party. Each party has 1BTC they staked. You transact a bit, and you are now owed 1.98BTC, and the other party gets 0.02BTC. The other party submits an older version of the transaction that pays him 0.03BTC and you 1.96BTC (at a time when fees are low and he gets it in for 0.01BTC fee). You now have the option of taking his 0.03BTC, but fees have gone up and you’d have to spend more than 0.3BTC in fees to claim your money back.
The solution to this is to ensure payment channels are always in a state where there is an effective punishment for cheating. You must always make sure the channel is not completely depleted for someone, else they have no risk to cheat. Make it risky for them, and at least to the point where the worst case is you send the entire tx as miner fees, and they are less likely to cheat.