"We argue that in the future, Lightning will likely rise in price in comparison to on-chain Bitcoin."

Why do you think so? #Bitcoin on #LN is "cheaper" to buy at most exchanges that support both layers. Let's say, you buy $100 worth of sats at Kraken. If you withdraw over LN, it's #free, if on chain, you pay $1 (?) fee. It means, LN bitcoin is about 1% cheaper for you.

Why will this change? If LN bitcoin becomes more valuable, large companies (banks) will see the opportunity and become custodians. More competition will push the "price" to the on-chain level.

Another L2 or a sidechain like Liquid will be competing as well, some people even use Liquid to get cheaper LN liquidity than going directly already.  

 Right, we agree with your analysis that Lightning is cheaper to get right now due to withdraw fees and this is why it has more utility and therefore value in our eyes.  Please read the rest of the article on how this can diverge in price from market makers such as Kraken. 

 I got it, in your scenario the #dollar become shit and #Bitcoin will shoot up. The main chain fees will be over the roof and people will prefer #LN. But, it doesn't mean, LN sats will be more expensive. Like I'm not going to swap ALL my corn from on-chain, most people won't. We will earn and use LN and #Liquid sats, while treat on-chain as a savings account. 

Let's say I earn/save up 1 #BTC on LN. Now, the on-chain BTC costs only 0.8 BTC. What will I do? Buy that shit straight away. The price will get to the same level because most of people will be willing to do so.  

 For large quantities like 1 whole bitcoin sure.  As the price of Bitcoin rises to the moon, the threshold for the size of the quantity you'd want to do that with will increase.  This would price the average user out, who has never touched 1 full BTC, and make it predominately market makers who'd charge a premium above pure conversion cost.

Therefore, we argue that investing in Lightning now, at the same price as on-chain to arbitrage it is low risk with a decent chance at payoff.