Portland has no single lottery site. Multnomah County posts affordable homes with openings, the Portland Housing Bureau lists the buildings on its N/NE Preference Policy waitlist, and Home Forward opens its waitlists a few weeks a year.
Most openings are first come, first served: you call or email the property and apply with its manager, not with the County.
Each home may have an income limit (a share of the area median income) that depends on household size.
The manager checks your income, rental history and background before you can sign a lease.
The official site is Multnomah County housing openings. Its rules decide.