Bose has introduced the SoundDock Series III digital music system ($250), which is compatible with the Lightning connector and built for the iPhone 5, fifth-generation iPod touch, and seventh-generation iPod nano, but not iPads. It’s the newest edition of Bose’s SoundDock Series — the original SoundDock debuted in 2004, followed by the SoundDock Series II in 2008, as well as the SoundDock Portable in 2007 and the SoundDock 10 in 2009.…