I'd check the NPS closer to your planned dates as things do change, but from what I saw, Lone Rock is normally open year round. The water gets shut off for the winter October 31st and that likely means no restrooms/showers or refills for the holding tanks. And with water levels so low, the rock may well be high and dry. :(

This campground is open year round. Dump station and Potable water will likely be unavailable due to freezing conditions.

You can camp year-round, but potable water, the dump station and trash collection are seasonal. There is a self-serve pay kiosk at the entrance. Click "Official website" on the Campendium page.