We were able to fill up our tank with potable water for $10 at the Boulder Creek RV resort, which is on the south end of Lone Pine. It’s very close to the campground, and the staff there was helpful and accommodating.

The water available at the Campground isn't potable because they don't test it but it's good for some things of course. I would just go into town to a gas station were it sometimes available before you head up to sites. We used the Campground vault toilets to conserve both water and black tank space.

They usually turn off the campground water and close the dump station for winter, but timing varies. If the water has been shut off, you'd need to go into Lone Pine (about 5 miles) and try the shell or mobile gas stations. Alternatively, you may have some luck at Boulder Creek RV park, a few miles south of Lone Pine