Legally, the statutes do require that the LL perform the extermination when it's a multi-family housing (as opposed to a single-family house), and it looks like your LL is trying to take care of it. For what it's worth, I boarded a cat many years ago when I rented an apt, and it became infested with fleas. I would put my arm on top the carpet, and I would literally see 3 fleas jump to my arm. It was a huge problem, but I didn't think I could hold the LL responsible at that time (I was ignorantly bliss before going to law school). I hired pest control, which sprayed the entire apt. I never saw any bug in that apt ever since.
Back to your case -- if they don't solve the problem you can send a 7-day notice to terminate.
I agree with the advice of my colleague on this matter. The best course of action is to wait to see if the problem is resolved. If the problem is not rectified you should give the seven day notice to terminate the lease. I highly advise you to seek the assistance of an attorney when doing so because there are certain statutory requirements that must be met to avoid the possibility of being sued in the future. Best of Luck.
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