You're correct, Cruise is using LIDAR and RADAR systems. I used to work on Google's Waymo project, and Cruise is using almost identical tech in their SDCs (so much so that I believe there was actually a lawsuit about this), so I can speak to this a little bit.
These cars use LIDAR, RADAR, microphones, cameras, and a few other sensors to get an accurate readout of their surroundings. The LIDAR is used mostly to determine the shape of things around it (and thus determine the type of object it is), and the RADAR is used to calculate the trajectories of those objects.
The cameras aren't used for measuring 3D space (which is what Tesla is doing, and is a major part of the reason that Tesla's Autopilot is so laughably terrible in the SDC industry), but mostly for identifying traffic lights and street signs. Detection of pedestrians and other vehicles is done mainly by the LIDAR/RADAR systems, and these cars can still identify and avoid pedestrians and other obstacles with these even in the event that all of the cameras have failed.
That said, the resolution of the cameras is still very decent. At the time I was at Waymo, the cameras were broadcasting to us in a crisp 1080 resolution (though I believe they recorded locally at 4k), even with the IR night-mode enabled. So to @swope's comment, the other car's plates were almost definitely captured.