I'm afraid that's not going to happen. If fees reach 1000 sat/byte again, opening and closing a LN channel is going to cost $25 or (much) more. That won't be worth is, just like I couldn't use Bitcoin for normal transactions at the end of 2017.
Yes, there is a thin ledge between "fees too high for LN" and "fees too low for LN".
However, the good thing is that opening a LN channel is not time-critical, so people can wait for it for moments with low fees. Let's say the fees for a instant confirmation rise to $50 at weekdays at daytime, but go down to $5-10 at night (western hemisphere). Then, observing the current mempool data*, at weekends it's likely that they go under $1 and cheap channels can be opened. And once LN adoption is boosted and many services using it, pressure on the on-chain fees should become lower.
But yes, I guess that if LN adoption depends only from fees, then it can fail, as fees could rise too fast and opening LN channels would be too expensive, like you wrote. So I guess there are additional efforts needed. Service providers, above all wallets and exchanges, should really realize that if they support LN now when fees are still low, they also contribute to a healthier and more sustainable Bitcoin ecosystem.
*For example, according to
Johoe, in the week between October 5 and October 11, fees were relatively high, with instant-confirmation rising over 100 sat/byte in several occasions. However, even in this situation at the daily minimum (night in the western hemisphere) they could always be confirmed for 8 sat/byte or even lower, and at Sunday 11, 1 sat/byte again was enough. So there were 2 (decimal) orders of magnitude between the minimum instant-conf fees and the maximum instant-conf fees.