I love Lost Park Campground. Beautiful area, but bring bug spray. Mosquitoes can be quite aggressive. My dog was even going crazy because of them once.
Yes, early June could still have some snowpack. We have received a good bit of snow lately, but we’re also seeing some pretty warm temps between snowfalls. It could go either way. We’re still about two months away so I can’t speculate on which way it will go. If, however, you’re comfortable with hiking in some snow in the higher elevations you should be able to find campsites without snow lower down, where you’d want to be for water anyway. I doubt it would be impassable. Brookside/McCurdy tops out at 11,800, but is pretty exposed and SW facing so will get a lot of sun on it.
It might be a good idea to contact the ranger district as it gets closer. I don’t hike that area very much as I moved farther into the mountains, but I’ll keep an eye on it and will dm you if I have anything worthwhile.
one or more gifts or other benefits from the co-op.