Miami-Dade County is offering a lottery for three families to receive $150,000 in down-payment assistance through the H.O.M.E. program. Eligible households earning less than 140% of the area median income can apply from Sept. 1 to 30 or until 200 applications are received. Winners must finance the purchase within 60 days. The townhomes, located in South Dade, have 3-4 bedrooms, no HOA fees, and range from 1,400 to 1,800 sq ft.