ASPs would proactively manage liquidity - they have visibility into the flow of funds from expiring pool transactions, and would likely pursue lines of bitcoin credit to bridge times of low expiration flow.
The ASP can also manage liquidity fees to discourage users from making high liquidity requirement payments in times like that. For example spending large vTXOs costs more liquidity than spending small, so the ASP may encourage users to consolidate their small vTXOs to make payments at times of low liquidity. Opposite of on-chain bitcoin in that way where ASP fees being high means its time to consolidate, and ASP fees being low means it's time to consume large "costly" vTXOs.