I have used Zerostats for about 50 years, and they definitely reduce static on my LPs. I can test the static by using a small piece of styrofoam taped to a thread. If there is a static charge on the LP, the styrofoam will cling to the LP.
I believe Zerostat recommended this way of using it on an LP, and it's what I do:
Holding the Zerostat about 12" away from the LP, I shoot it sequentially at three spots on the circumference of the LP; then I shoot it at the center of the LP, but point it away from the LP before releasing the trigger on that final shot. If I'm holding the LP and doing this, both sides get destaticized from treating just one side, in contrast to what @lewm says above. (I actually only discovered this yesterday by testing each side with the styrofoam.)
Now, I should mention that the humidity in my home is kept at about 50%, and most of my LPs are treated with LAST preservative, which seems to reduce static. I also have slit the sleeves of most of my LPs, so that the sleeves can be opened like a book to remove the LP. Perhaps, results would differ in a dryer space (more static) or with LPs that are not treated as I described.