Inyo N.F. has to prevent adding alternate leaders to prevent scalpers from winning lottery permits, and then selling them. That situation occurred with Half Dome permits.
All your friend can do is go to Recreation.gov and release her permits, and the system will then make the permits available online at a random time in the next 24 hours. Here's what I'd do as a first try: She should release them at a time when online activity is likely to be low (on message boards it is Fridays -- must be people getting ready for the weekend.) I'd suggest late Thursday night. Then you should coordinate with her, and set up a link/bookmark to the recreation.gov site for the date of her permits (here's July 1)
, and check as often as possible for those permits, say every 30 minutes starting in the morning. I would think your chances of accessing them are good.
If that doesn't work, I would still plan on doing the hike and make all the arrangements. Keep checking recreation.gov for the date you want, (especially
in the two weeks before) and watch for other permits to come available. It is likely that a few good people will sign on and release a few slots in the days before the hike.
If that doesn't work: Go for the walk-in unused permits. If you check the 2012 Unused Whitney Permits
info, you can see how permits went unused -- even after all the walk-in people were given permits. If you go in the day before the day hike, or the day-of for an overnight hike, you are likely to get the permits you want. As other groups pick up their reserved permits, they often drop a slot or two, and those become available right away. (I'd suggest being there at 8:30 for those, and check back every hour.) At 2 PM the day before (for day hikes), and at 11 AM the current day for overnighters, the no-shows are declared, and that block of permits comes available.
There are always group size reductions and always no-shows, so you CAN get permits. You just have to work at it.