Sorry, I meant the permits. If you look at the link and go down to J34: NF Lone Pine Creek. Those are the dates that are filled up. As far as Iceberg Lake, it will usually be thawed out by mid July and more than likely completely thawed out by August.
Reservation availability:
http://www.fs.fed.us/r5/inyo/recreation/wild/otheravail.shtml Other helpful links. Don't pay attention to the GPS coordinates link. You don't need them anyway:
http://www.whitneyportalstore.com/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=1;t=002524
http://www.mt-whitney.info/viewtopic.php?t=126