The number of nights is completely irrelevant to the lottery process. All that matters is that there are enough open slots available for the date you start your hike.
Once you have the reservation, when you go to the Visitor Center (S. of Lone Pine) to pick up the actual permits, it is THEN that they will ask you for the approximate number of nights. And even then, it does not matter that much-- it is only for statistical purposes and also if you are reported missing, they can get an idea where and when to start looking for you.
