Realistically faster sensors should be used to detect obstacles. LIDARs I could find with some cursory googling can run up to 15hz. Computer vision systems can run much faster (I have a little JeVois camera that'll do eyeball tracking at 120hz onboard, I assume something that costs more can do better).
But more importantly, you're vastly trivializing the problem - Standing right in front of it, sure the LIDAR will see the person no problem. Standing 110 feet away (which would be min stopping distance at that speed)? Realizing that, for a LIDAR with a 400' range at 15hz moving at 40mph you get ~7 samples of a point before you're at it... For at least the first 3 frames that person is going to look like sensor noise. At 110 feet that person (which I'm calling a 2' wide target) is 1 degree of your sensor measurement.
It's not that it's useless or broken, more just this a seriously bad case where optical tracking couldn't work and where LIDAR is particularly ineffective at seeing the person because of how it works. More effective might be dedicated time of flight sensors in the front bumpers, unsure how long a range those can get, but they are also relatively "slow" sensors.