Sensor to measure distance of moving object
Ultrasound. You've already mentioned this, it's probably going to be the best choice.  I would be surprised if ambient noise was a big problem, but it does depend what that noise is.

Lidar. You mentioned this one too.  I don't know much about it but I daresay it's expensive.

Laser triangulation. I would expect this to have the same advantages as lidar, but be cheaper.

Light gates. Cheap and reliable, but probably poor resolution unless you buy a lot of them and you have to put transmitters/receivers on both sides of where the car is going.

Capacitance. You can have a large panel on the wall and detect the distance to a (metal) car or truck.  I've seen it done, but it's probably not a good choice for most of the time. Different cars will produce different responses.

Image recognition. Probably only cost effective if you already have CCTV in place. But modern computerised image recognition can achieve a lot more than you might think.