1. (smaller effect) If multi-sig users start using Schnorr instead after activation of it.
2. (biggest effect) If we move the traffic from big bitcoin exchanges to lightning network. If you look at each big fee spike in history they are almost always happening because bitcoin price either goes up A LOT or drops A LOT. That means the extra on-chain transactions are from traders. If that is moved to LN the on-chain capacity is left for other transactions. Not to mention the ability to deposit/withdraw bitcoins in an instant with virtually no fee while being in full control of the keys instead of having to leave them on the exchanges.
I hope that at least the withdrawals from exchanges will become smaller. That would be your [1] I guess.
I know that big variations in price make tx fees go crazy. I've suspected the arbitrage traders/bots, but it's more than that. However, as long as LN is "advertised" as beta, unfortunately the exchanges can easily make a point of not adding the LN support. And even afterwards it could be difficult to get all of them use LN (I'm sure you remember the we had the same with the adoption of SegWit).