If you want remote in Lassen…
Stayed at Butte Lake for two nights in late June 2022. None of the campsites has an unobstructed lake view, but it’s a short walk to the day use area on the shore. This is a good jumping off point for a ton of hikes on this side of Lassen NP; excellent signage tells you how far each destination is. The sites themselves are not very private; kids were rolling through our site on bikes all afternoon and evening, dogs were barking at each other, it was a little crowded feeling even though it was probably only at half capacity. (There were reservation cards on almost all the sites, but it seems like a lot of people didn’t show up.) That said, after driving past some of the other campgrounds right next to the highway, I was happy to have chosen this one.