Verified answer

The new roommate has to sign a lease, which will expire when the original lease expires. Your landlord can not raise the rent more then the 5% a year that LA allows. The lease may allow the raise within the lease term, say every January, but has to be specified within the lease.

If you live outside of LA proper this will not apply to you, they can raise the rent as much as they want. The rent control is only within the city limits of LA itself, not the LA basin.

In most rental agreements, EVERYONE living in a place MUST be on the lease.

Los Angeles city has rent control. The answer to your question is complicated. Contact the city rent control office for help.

What does your current lease say, and who signed it??