East Los Angeles isn't its own city. It's an unincorporated part of Los Angeles County, so LA County Public Works issues building permits for homes here, and you ask its local office what your project requires. Don't assume a lift goes without one. We check with the County for your address before we set a date, and when your job needs a permit, we take care of it and the inspections that go with it.
Most of the cities around us, like Montebello and Monterey Park, run their own permit counters, so the office changes once you cross the line. We're based in East Los Angeles and work in those cities, Downey and plenty of others nearby, and we sort out the right office before anything else.
Most of the county's mapped soil rates Low for shrink-swell, a measure of how much it swells when wet and shrinks when dry. That's the county as a whole, not your lot, so when a house here has settled I check your own lot first. We see plenty of older houses on tight lots with walks and drives right against the walls, where roof water and drainage are the first things to check.