I hiked Mountaineer's Route 9 times beside another 5 attempts. In 3 cases I was the beneficiary, in a group of 3 people, of the walk-in permit lottery at 2PM for the next day permit if I recall correctly. That time I understood that a permit become available, w/o cost, if not confirmed before 11AM the previous day. We got, from Bay Area, at the Visitor Center before 1PM Saturday, we applied for the walk-in lottery and at 2PM we won the permit for next day, "day-hike" on Sunday. I applied in 3 cases and I got the permit in all 3.
In my case walk-in worked fine. I'd hike Mountaineer's Route this year too. I am for walk-in permit lottery.