It sounds you are in Texas. According to Texas law, lanloard has the responsibility to provide a habitable dwelling unit. The lanlord shall make a diligent effort to repair or remedy any condition that materialy affects the physical health or safety of an ordinary tenant ( not specific one) . If it is not listed in the lease, you should consult with a real estate attorney to determine if your situation makes you unhabitable and unsafe, then you can either call a contractor to eliminate the animal from the attic, or send notice to terminate the lease as you did. A lot of time, a letter from an attorney will make the landloard responses quickly and positively.
Good luck!
