Resolved! On my STM32L476RG, my LPTimer does not work when in STOP1 mode.
At startup I do initializations, then go to STOP1 mode. Initializations include setting a wakeup in the RTC and setting the wakeup clock to the MSI clock. The RTC successfully wakes the MCU. In the wakeup callback, I do some things then start a LPTIM...