Rico, the lottery is ONLY for people using the Mt Whitney Main Trail, starting at Whitney Portal.

Cottonwood Pass and Cottonwood Lakes (and even Kearsarge Pass from Onion Valley) are all on a quota system, where 60% of the permits become available at 7 AM 6 months before the hike start date. The remaining 40% become available 2 weeks before the start date (not sure if it is 7 AM, or at a random time that morning). The 40% are supposed to be "walk-in" availability, which before COVID was the case -- they became available only to walk-in requests at 11 AM the day before the start.

Lately, those permits coming available at 7 AM are gone in seconds, due to their high demand. They are all handled via Recreation.gov.