There are not many formal Lightning Network case studies yet. We anticipate that there will be several areas of initial development.
Lightning offers early promise in countries with failing fiat currencies such as Venezuela. This is also an area that would allow rapid adoption once local currencies begin to fail.
Micropayments enable entirely new business models but have never developed because current payment methods have too much friction in both time and cost. LN offers a means of experimenting with those new models.
There are numerous fiat-based peer-to-peer payment applications: PayPal, Venmo, WeChat, AliPay, Square, and others. There are two likely paths for LN development in this area. Existing p2p apps will add Bitcoin and/or LN satoshis as a currency. And new vendors will launch LN based p2p payment apps. Crypto has several inherent advantages over fiat p2p apps: lower friction, universal currency, privacy, and ubiquity.
Here are some possibilities we are monitoring.