I highly doubt it (but I am not a lawyer). It sounds like this landlord is trying to pull a fast one.
My advice is to talk to a lawyer-- it is generally easy to get free legal advice for these types of questions.
I did a quick search for "tenant rights" and "tenant legal aid" in Los Angeles. This link looked promising.
Housing Rights Center
You could call and talk to them. If they can't help you, they can refer you to someone who can. I imagine all you need is a lawyer to advise you to tell the landlord to take a hike, and this shouldn't take very long.
You might also try the Department of Consumer Affairs.
I sure as heck wouldn't sign a new lease when I had a perfectly good old one. I might offer to make a notarized copy of the old one if the landlord paid for the expense.
I can't think of any circumstance that an increase in security deposit is justified.
But, it wouldn't hurt to talk to a lawyer.