Actually, the daily quota for overnight backpacks on the North Fork is 10, and only 6 are reservable. The other 4 come available to walk-in people at 11 AM the day before the hike. Here's the Inyo Quota page. North Fork is "J34"

You can get those 6 permits in February -- just be the first to log onto the Recreation.gov site on the 6-months-before your entry date. I think the permits become available at midnight Eastern Time (9 pm the night before, here), but not sure of that. You should try one of these evenings and see, as a practice run. Then on the night you need, be there clicking the "Update Availability" button, and be ready.

Here's the Recreation.gov link reserve North Fork J34 overnight permits.

Once you reserve the six available, you can get the others needed on the morning before your hike if you show up at the Interagency Visitor Center south of Lone Pine (where you would be picking up your reserved permits anyway). Be there at 11 AM, they hold a drawing to see who gets processed first. That applies to people picking up reserved permits as well as anyone trying for walk-in permits for next-day overnight hikes for all trails, so there would likely be a small crowd.

...will write more later....
edit: changed the online availability time.