Nope. The Lidar pulses are encoded uniquely to each sensor, so one sensor can filter out an (already unlikely) direct hit from another lidar. The cameras are IR filtered and also unlikely to get hit by the lidar. Radar is pulse encoded in a similar way to lidar, although possibly more likely to lose performance if surrounded by a lot of other radar units. In general, dirt on your sensor lenses is a lot more annoying than interference from other cars.

Interesting. Do you have any good links to more information about how this works in practice? I guess it's similar to CDMA cell phones.