As long as the person is the only person renting a room, she is a lodger. You have two options: 1) serve her with a 3-day notice to pay rent or quit; 2) serve her with a 30 day notice since she is paying month to month. If she doesn't move out, she is a trespasser and you could enlist the aid of the local authorities to eject her. No unlawful detainer is required. Good luck.
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Because she is technically classified under California law as a "lodger" you can give her a 30-day notice and then have her evicted by the sheriff as a trespasser when she doesn't leave. Also, because she pays late, you can issue a 3-day notice to pay or quit on the basis of non-payment if she doesn't pay on time next month. However, if she doesn't leave and you proceed to filing an eviction action against her, she could potentially drag it out for a few months before finally leaving. The 30-day notice to evict her as a lodger sounds like the best tactic to me.
Kevin King, Principal- Essential Law Services. HTTP://ESSENTIALAW.COM, 415-562-6862. The information presented here is general in nature and is not intended and should not be construed as legal advice for a particular case. This post does not create any attorney-client relationship with the author of the question answered. For specific advice about your particular situation, consult with me or another qualified attorney off-site.