How well does LPS lighting work in foggy or misty conditions? 

It's blooming fantastic.!!!   
That's one of the reasons it was first adopted.

Indeed. Not only does the high luminous efficacy make them economical to run, the fact that the light is monochromatic means that it isn't scattered by mist and fog in the way that white light is. They make it easy to determine moving objects such as cars. I for one would rather know that there is a car on a collision course with me than that the car that just hit me was red 

And that's a big problem with LED streetlights. In my opinion, LEDs are unsafe, short lasting, glary and barely more efficient than HID or LPS. 

Thanks for the answers, y’all! Much appreciated!   
P.S. Imagine a house surrounded by a red mist... The LPS would render it a non-problem. 

And that's a big problem with LED streetlights. In my opinion, LEDs are unsafe, short lasting, glary and barely more efficient than HID or LPS. 

The discontinuation of SOX lamps in favor of LED will lead to more and more car accidents.

The discontinuation of SOX lamps in favor of LED will lead to more and more car accidents.

..if it didn't increase already with the HIDs being changed. 

A common use for SOX over here was tunnel entrances, with the idea that the monochromatic light would help visibility at the entrance due to the fog that tends to form there. Now, I've seen some tunnels retrofit those lights to LED which defeats the purpose of having SOX at the entrance.