Almost certainly not manufactured by the "Complete Shop Outfitters" who were Leiman Bros. of 62 DL John Street, New York, the simple 8-inch swing plain-turning lathe shown below would have been bought in. Advertised in February 1915, who the maker was is unknown, but the lathe does bear a passing resemblance to the simpler ones from the German maker Boley--though it is much more likely to have been of American manufacture.
Interestingly, the seller offered "All sorts of attachments supplied at slight extra expense" thus hinting that the lathe might well have been the product of an established rather than a one-man-and-a-boy company. What a pity that the accessories are not listed, together with their prices, for a good slide rest assembly, of the compounded type, might well have added 50% or more to the price - hardly a "slight extra expense".