Is this campground a little cooler than right off the 395 in the summer? We want to stop partway to Yosemite, but it seems most spots will be high 90s to low 100s

Cooler indeed. In May we had 65 in the evenings when Lone Pine village had 80.

Comfortable at night in low 70s in late July

Ditto that. Altitude means cool.

Yes. But you'll want to camp at Whitney portal as Lone pine lake is actually a 3 mile hike in and camping ground. The other camp grounds not in the mountains are gonna get pretty hot.