I took a look at the area on MyTopo (click the "MyTopo" button on the map to see the topography).
You didn't say, so I'll have to assume you are taking the loop between Lamarck Lakes and South Lake / Bishop Pass.
If that is correct, then you will need a permit to enter either the Lamarck Lakes trailhead (J16) or the Bishop Pass trailhead (J21). Reservable quotas are 6 and 22 respectively, walkins 4 and 14. ( Trails and Trailhead Quotas )
To reserve a permit, call the Wilderness Permit Reservation Line (760) 873-2483. Walk-ins are available at 11 AM the day before the hike at any Inyo National Forest ranger station ( Locations here. )
It's an ambitious hike with three passes, but definitely a most beautiful area. One of my favorite spots on the JMT is McClure meadow, just a few miles down the canyon from the Evolution Basin.
Here's a video from McClure Meadow
Hut at Muir Pass Hikers often spend the night inside.