A Wilderness Permit is required for just about all trips in that part of California, either in the National Parks or in the Wilderness areas outside the parks.
Now, a permit can be easy or it can be difficult. If you are trying to get something for a group of people, for the prime season, for a Friday or Saturday start, then you might run into a quota problem. Therefore, a permit reservation costs a few bucks, but it is worth it in reduced headaches. By contrast, if you are trying to get a permit for only one or two people for a mid-week start, then it isn't nearly so hard. A reservation still would not be stupid, but it isn't always that essential.
I often go to the permit station in Bishop, and I make a point of being the first person standing in line for when they open the office on a summer morning. That way, I have never been aced out of the permit. If I show up at 9 a.m., then there is a waiting line and the daily quota is already gone.
I've gotten excellent results out of the on-line permit reservation system. You still have to go to the permit station to pick up your permit, but at least you will know that you will get it.