The Housing is Key program is a partnership with the city and the California Department of Housing to expedite checks to qualified applicants.
About $260 million will be allocated by the city for this second round of relief funding.
Officials say they are also expanding eligibility to allow more people stay in their homes.
In the meantime, California's eviction moratorium remains in effect until Sept. 30.
Locally, protections against evictions will remain in place long after that.
"The eviction moratorium is not going to end," said City Councilman Kevin de Leon. "It will continue, at least for another year, when we terminate the emergency rule for the city of L.A."