"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.