The conversation is complicated because LIDAR is used for many purposes in self driving. It's used for localization, it's used for objection detection, it's used for classifications, it's used for understanding occlusions, it's used to get accurate 3D positions and speeds of objects, etc. For each of these cases there is a way to use just cameras (or camera augmented with radars), but often with some significant performance penalty.
One of the big challenges is that most self driving stacks have an interface between the perception and planning stages that is specified to be a 3D model of the world. LIDARs are particularly helpful at creating 3D models because that is essentially their native data product. So, for "traditional" AV stacks that use this interface, LIDARs are bound to improve performance a lot.
If you use a different approach, say pure imitation learning off of sensor data, you might find that LIDARs are not as important. (intuition: Humans drive well without understanding super accurate positions or velocities of objects.) Though Tesla isn't taking a pure imitation learning approach (yet), they are more in line with this strategy.
All this said, I don't think that having or not having LIDARs is a major factor in the progress of self driving. It's just a way to use money to improve perception performance (and reduce data labeling cost!) but neither is the major blocker for the industry. If we extrapolate from the last 10 years of progress, it seems like high-level self driving is going to take a while and I think that it's likely that LIDAR prices will have fallen dramatically by then and we'll see them as part of the overall sensor constellation on most vehicles.