Here’s an example of L9 pay on a LC day:

Scheduled for a 1 leg day, FL shuttle -> ATL, blocking in around 2200 on last LC day. In flight rerouted to operate ATL 2230 -> LAS 2345 (0245 base time), then DH LAS -> ATL on the X day.

The duty period on the LC day interrupts the X day. The next duty period interrupts the same X day. 23L9 is paid for both duty periods.