Complex sentence: However, Flava Works filed a lawsuit against the City of Miami in response to the verdict, invoking First Amendment rights and arguing that was is not running an adult-oriented business out of the House Next Door.
Split into simpler sentences: However, Flava Works filed a lawsuit against the City of Miami in response to the verdict. They filed the lawsuit due to citing that the ruling invoked First Amendment rights and argued that it is not running an adult-oriented business out of the House Next Door.