We used a dump station on our way home in Big Pine at the Mobile gas station, ~42 miles North on the 395. This was a matter of convenience and we didn't bother checking for anything else around Lone Pine. We normally fuel up in Big Pine there prior to arriving and clean out on our way home. Water pressure, space, and cleanliness was a big factor as well. If you're coming from the North or going home, this is a good option.

Tuttle creek off of horseshoe meadow rd.

I used the RV Park just south of Lone Pine.

Sierra Vista RV Park in town, or Boulder Creek RV Resort, further south of town... All for a price of course... HTH