If you have any automation applications that have icecast2 compatible encoders then you can already connect to Live365 servers.
You would need an encoder|application compatible with Iceast to stream a 'live' broadcast. Here are several options that are free or low cost:
Nicecast - Free Demo for up to 60mins then Nicecast will insert a sound block. 40$/one time payment.
Virtual DJ - Virtual DJ has a "free" home use version. To unlock the streaming portion you will need to have a license. With Virtual DJ you can do a one time payment ($299) Or a monthly subscription (19$/month).
LadioCast - This is an Icecast compatible encoder that is free.
Broadcast Using This Tool Another free Icecast compatible encoder for Macintosh
Megaseg - Not free but a low cost (comparatively speaking) Automation and live mixing application for Macs 99$/one time purchase.
Please note, which ever applications you choose, when streaming music, the application will need the ability to send Live365 the metadata of the track (song title and artist) to keep your broadcast legal.