The page of LA's Planning and Zoning Code is down right now.
Here's the link so you can try later.
I expected to find a Building or Housing code section but did not.
Some city codes are easier to search than others, so it may be easier to just give 'em a call:
The phone number for "Building and Safety" - which I'll assume is the area to speak to - is 888-524-2845.
Since you may get bounced around, keep it short, as in:
"I want to add a sidewalk to my sloped yard and want to know if there is a code requirement for a step."
That ought to get you to the right person.
And by the way, if you want to keep hunting for the answer on their site, Go to
http://lacity.org/, hover over the "For Residents" Tab, then click "Home Improvement and Construction".
The link I mentioned earlier was the one for "Planning & Zoning Code" but you may be able to find what you want by putting your property info into the fields at the "Property Zoning Information" link.