If they exit the wilderness overnight, their old pass is no longer valid. The Walk-in permit is almost the only way, unless they happen to call in several days before and there just happen to be some phoned-in cancellations available. They can reserve these for $15 per person.
But if you check the August day hike unused numbers
for last year, you can see that except for Saturdays and Sundays, getting a day hike permit is a pretty sure thing. Even on the weekends, if they get to the Visitor Center at 2 PM when they draw the numbers, they have a great chance of getting a permit.
As for the walk-in permits, since they will be hanging around the east-side, they could get an overnight permit a day or two before your expected arrival, and pack in just to Lone Pine Lake, and set up camp there. As long as they used their camp overnight each night, they could hike up (or back out the trail head) each day and the overnight permit would remain in effect.
All that being said, unless you have a Spot Messenger and they have computer access, they might have a tough time gauging exactly what day you will arrive at the summit.