Livestream is just a service provider, they're not the ones producing the content you see there. They're just aggregating it and providing the bandwidth.
There are lots of people doing live streaming of concerts, including major broadcast outlets, startups, venues themselves and others. NPR, Concertwindow, Jazz at Lincoln Center all do live streaming for instance.
There are many services that provide video hosting, Livestream being one of them. Livestream has recently changed their offerings and business model a bit to a no-ad service. They do have a paid service, as most pro services are of course.
Big picture, you just need to get audio into an encoder (that's doing both video and audio encoding). The best way to do that will depend on your specific requirements and only you can decide.