Unless the lease has an auto renew feature that will renew it unless the LL receives notice of intent not to renew, the LL is out of luck. If no auto-renew, then the lease is for a term specific and at the expiration of that term the lease automatically terminates.
The reality is that the LL is probably trying to bluff you so he can keep a portion or all of your deposit. Don't fall for it. When you turn in your keys, under California law, he has 21 calendar days to notify you of any damages in writing or return your entire deposit. If he doesn't then he waives any right to keep any of the deposit. Take pictures, lots of them, of your apt so you can document the condition after you move out.
It sounds like you could possibly have a bluffing LL so make sure you have plenty of evidence to refute anything he might say.
I hope this helps.
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