It reads like a "non-compete agreement" clause.
Section 16600 of the California Business and Professions Code states that "every contract by which anyone is restrained from engaging in a lawful profession, trade, or business of any kind is to that extent void."
My guess is that the language you quoted above could not be held as enforceable in a California court. Most of these "non-compete" clauses are usually found in business or employee contracts. That yours appears in a real estate contract is interesting. But Sec. 16600 would still apply to a leasing agreement (which is what a lodger is, a lessee). Deeper legal research might be necessary to see if the courts have handled this question before.
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I think the best thing for you would be to see an attorney who can review your contract and answer your questions. Without reviewing the entire contract, it is hard to give you an answer.
Commercial real estate Property rental agreement Landlord or tenant Renting a house or apartment Lease agreements for renting Breaking a lease agreement Real estate Employment Non-compete agreements and employees Termination of employment Employment as an independent contractor Court orders