Yes, there is a dump and water fill at LHSP that is open to noncampers. But dont count on just being able to use the facilities at any time. We needed to dump tanks after BLM camping nearby and were told we would have to wait until after noon. So, since we were headed south, we dumped tanks at Cattail Cove SP
During normal times, they charge a fee to use the dump station. During busy times, especially on departure mornings, they sometimes deny access unless you are staying overnight.
Yes, there is fresh water fill there. There is only one fill (on the wrong side of the road, at that) and two dump lanes, so it can get pretty backed up. It was not designed very well.
Yes, RVs outside of the ones staying there can use the dump station (with potable water) for $15. However, they aren't allowed to access the station until after check-out time (at which time it becomes very busy). If your schedule allows it, I would use it later in the afternoon.