By the way, I'm 49 this month so quite a bit older than you. I have been training Muay Thai about 3 times a week for the last couple of months and have lost 10 kilos. So, if you're looking to get fit and lose weight, just go. No need to build fitness first. I've heard people say that before and they never get round to starting.
You don't need to build fitness before going. They will help you build your fitness no matter what level you are at. And you don't have to go running before class either.