If you think that LN is still far from being widely used, then the role of this protocol is almost non-existent in terms of influencing the next bull run. Let’s be honest, the average user still doesn’t know what SegWit is, not to mention the native vs. nested versions, and LN is even too complicated for slightly more experienced users.
sure but how much trade do average users conduct on exchanges? The clients with the largest amount of trading activity will also be on the more sophisticated end of the scale when it comes to technical abilities, and regular traders are more incentivized to cut down marginal costs of business (represented here by the risk of keeping funds in exchange controlled accounts and trading/depositing fees)
All such friction can be done away with if a p2p trading platform implements Lightning. This would mean first solving the costless call options problem, which is inherent to the HLTC-based channels that power the lightning network. If that happens (maybe someone already has?), then a blazing fast p2p marketplace could enable near-instant inter-cryptocurrency trades settlement, putting centralized exchanges at a significant disadvantage when it comes to setting the price of cryptocurrencies (imagine a trustless version of the old shapeshift website if you don't understand what I mean).
Such a platform would then force the more questionable centralized/fiat exchanges to introduce Lightning deposits too. This would help to shift the volume of cryptocurrency trading completely away from the exchanges who comply with regulation regimes, and so I imagine they would eventually find some politically expedient way of following suit, or lose their influence (and thus importance) in the marketplace.
I don't see the final stage of these predictions taking place before the next bull run, but it's not even a sure thing that we will see a bull run when everyone is expecting it (indeed, it's perhaps more sensible to expect it when the general sentiment is against it)