The handheld is indeed the control unit - its function is the same as the more-elaborate CAB-1/CAB-1L/CAB-2 for the TMCC/Legacy systems.
It is my belief (I do not own any) the LionChief locos/sets all come with a small wall-transformer for power. This is sufficient for their intended use - but you can put it on your "regular" track/transformer layout, too, and run it with the handheld that came with it.