Assuming your case is an unlimited civil case, which almost all Unlawful Detainers are, you have 30 days from service of notice of entry of the judgment. Note that the time is not extended for mailing. If no one serves a notice of entry, you have 90 days. The time changes if someone serves a valid motion for new trial or motion for reconsideration.
These periods govern every court in the state, not just those in Los Angeles.