Apart from the ends of their beds being stamped Graham-White MFG. C^o Roanoke VA and with a serial number (that must have started at 1000), nothing is known of this manufacturer as far as lathes go. There is a Graham-White Company in Roanoke (a town in the Blue Ridge Mountains of southwest Virginia) that was founded in 1914, but that is involved with railway, truck, bus, and industrial work.
While not as common as other American lathes made for watchmakers, numbers have appeared online in recent years. However, none have been found in a fitted case with accessories; instead, all have been single lathes with motor drives.
Of the heavier  WW (Webster Whitcombe) type, the Graham White has the usual 50 mm centre height and takes 8 mm collets in the headstock. The example shown is mounted on one of the popular Borel cast aluminium stands with rubber-buffer feet, making it a self-contained unit that can be lifted on and off a bench as desired.