LIDAR gives you precision distance measurements. But LIDAR helps you little, if anything, with object classification. And object classification, the understanding what the car sees, is the big challenge with self driving.
Yes, with semi-intelligent systems it gives a head-start, as you can reasonably easy detect obstacles, but it does not help in understanding how to react to the detected obstacles.
So I would consider LIDAR rather a system which at the current state of development helps with collision avoidance rather than with true self-driving.
Here is the issue: Video cameras will work properly most of the time but once in a while the exact distance will be wrongly calculated as can be seen with all the Teslas crashing in trucks lately. A LIDAR gives you a way higher confidence on the distance of objects.