no Internet service. Can I mirror iPhone to Apple TV?

That’s basically it. I turned off my cable modem service for this apartment, and would like to play music and stream video from my iPhone, for which I have “unlimited“ data, to my Apple TV so I can watch on a decent size screen. Is there any way to do this? I spend most of my time in another city, and don’t want to pay $1000 a year for internet the few weeks I spend in this city. If not, is there such a thing as a lightning to HDMI cable?