Some of the functions of a waypoint mission are sent from the app such as the interpolate option where the camera can be moved up or down autonomously whilst flying a mission, the interpolate function relies on a connection between the quad and the app without a connection the interpolate function fails to work .
as the lights can be controlled via the app in litchi then it stands to reason that the app could send extra commands such as turning on the lights, the same way that it can tell the camera to move using the interpolate function.
The term app connected translates into an FPV connection as the app communicates through the FPV connection and not the normal flight control connection.
So again I say that yes Litchi should be able to do it.