Tsunami,
If you are talking about doing the Main Whitney Trail, a dayhike permit is required 365 days per year. How you obtain it (via the lottery process or via self-issue at the Lone Pine ranger station) depends on when you want to do the hike. During the non-lottery season, you can just self-issue. During the lottery season (May 1 through November 1), if you have the scheduling flexibility to be able to just show up the day before a particular date that you know has plenty of unused permits still available after the lottery has played out (that info is not released until May 1), then that is an option. On the other hand, if you don't have that flexibility (you only have one or a very few specific dates on which you can dayhike), and you want to hike during the lottery season, then the only way to guarantee that you get the date you want, is to apply through the lottery process (and even then, it's not guaranteed until you actually get it). And so, when filling out your Main Whitney Trail permit application, it's best to submit a few alternate dates, just in case the quota for your main preferred date fills up before your application is pulled out of the "hat" for processing.
People who get caught in the Whitney Zone without a permit are both fined and turned back. Not sure what the exact fine is, but I have heard it is in the $200-$300 range.
CaT