Same issue here (Dell XPS15 - Win11 Pro)
Lightshot is running in the background (services in the task manager) but is not visible in the tray. it does not respond to any key combination. I have also disabled the print screen in the accessibility area to not use the windows Snipping Tool. I've already reinstalled Lightshot several times, always uninstalling everything and the downloading the latest version and installing from scratch but nothing. Laptop and Windows up to date with all updates.