Could I break my lease ?

my hot water in my apartment takes almost 2 hours to get hot.I am on a 12 month lease. My apartment had a total of two ownerships since I lived here the past 11 months. Both we're aware of my hot water problem. The new owners tells me updates on what they are doing in order to fix the problem, but to no results. I am a good paying tenant, I pay my rent on time. I even asked if they could exchange me into another apartment for the same rent price, they told me that they need more money. Plus, I want another apartment with a bigger bathroom because the only bathroom in my apartment is in my bedroom and company has to enter my bedroom just to enter my bathroom, and plus when you can sit on the toilet and wash your hands at the same time, and get jokes about it all year from your friends, I think its time for a bigger bathroom. My lease expires at the end of July . I haven't paid the rent for today yet , July 1st, which covers the month of june. I just placed an application today for another apartment somewhere else and they will let me know in a week if its approved for me to move in. If I get approved for the new apartment, do I still owe them for the month of june ? and plus, if im approved, when do I let the manager know that I'm moving so I won't have to pay him for the month of July ?