Horseshoe meadows is a one-night-only camping area, and I've never heard of it being full. I often drive over and arrive up there at 10 pm. If specific sites are full, it is wide-open bare ground, so you can just find a spot 50 yards away and lay your camp down.
First night at Horseshoe, then second at Outpost would be an excellent acclimatization plan, if you aren't too susceptible to AMS.
"Daily Lottery" occurs several times a day, and is just people taking numbers out of a hat, and lowest number gets first shot at the permit counter. At 8 AM you get the leftover no-shows from prior day--same as what was available at 4:30 pm previous day. At 11 AM, no-shows for overnight hikers entering current day become available. At 2 PM, no-shows for day hikers entering the next day become available.
Also throughout the day, no lottery, but whoever is at the permit counter: Any people picking up their reserved permits, if some hikers dropped out of their hike, so that releases a permit here and there: those permits become available immediately.
