Q: can I break my lease due to cockroach issues? they spray my apartment 2 time and the issue is still going on.

A: Probably not. While a vermin or insect infestation can be considered in determining whether there the premises is "UNINHABITABLE" usually it requires more than a cockroach problem that can be handled with an exterminator, as frustrating and inconvenient as this can be. What you might want to do is request the LL give you a rent reduction for the months that you are inconvenienced. If he doesn't want to, you can sue him in Small Claims for the difference between the rent and the value of the apartment as provided to you. This is a contract issue, you did not get the apartment you bargained for. You are also entitled to "repair and deduct" which means that, after giving notice to the LL of at least 30 days to take care of the problem, you can hire your own professional exterminator and get rid of the bugs, the cost can be deducted from your rent. If your LL attempts to evict you, it is retaliatory eviction and then you are entitled to some bucks. If you are living in high density housing (apartment house) the problem is not just your apartment, it is through the apt house, so just spraying your apt only drives the bugs next door and they return.

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A: Probably not grounds for termination as unpleasant as it is but certainly would suggest making a request to the Landlord for reduced rent for the impacted months until corrected.

This is a contract matter, you did not get the apartment you bargained for in your lease. You could repair and deduct which means that, after giving sufficient notice (see your lease.. typically 30 days) to the Landlord to take care of the problem, you can hire your own professional exterminator and get rid of the bugs, which the cost can be deducted from your rent.

Hope that helps.