I was in a similar situation a couple of years ago as the landlord. I realized on June 15th that our year lease was ending June 30th and I had neglected to either 1) give my tenant 30 days notice that I was terminating the lease; or 2) get my tenant to sign a new one. My tenant had also neglected to give me notice that she was vacating at the end of June. So, I sent her a note saying that we both had apparently screwed up on giving 30 days notice to the other, so that per the terms of the lease we were defaulting to a month-to-month situation.
The tenant was OK with this, but around June 25th said that she might be moving out at the end of July (our 1st extension month), but that she wasn't sure. I waited, and eventually the first week of July passed with no word from her. I sent her another note letting her know that since I hadn't heard back, I think we were in another 1-month extension situation. At first she was confused, but I went through the lease with her and we worked out the legalese together (I just use a boilerplate that someone gave me, so I was figuring this out as I went along). We noticed that in the event we enter a month-to-month situation, only the lease end date changes and all other terms of the lease remain, including the same requirement for one party to give notice to the other at least 30 days before the end of the lease (which was now July 31st).
Anyway, we went on like this until the middle of August when she finally gave me written notice, meaning that we extended the lease by a third month through the end of September.

