I agree with AL, this lathe looks to be more of a WW 1 area (if not older).
The gap in the bed, and the bottom of the beds design are good clues to watch for on brand/builder. I have never seen the design myself and it really doesnt matter what it is. Just use it, repair it, and use it some more. AT its age, any parts are going to have to be built, or hand fitted from other lathes anyway. Although I understand, to be able to show its brand is a plus.
And again as far as parts, in this style of lathe its almost kinda of a wash(hopeless) to find parts ( unless it is something very comon). And just about anything it could need can be made from scratch, or modified from a nother lathe to fit. Gears in the spindle drive, spindle bearings become a problem though if needed. I would tear the spindle down/aparts and inspect,clean and ajust before even using it much. Many lathes of this design will have felt oilers in the spindle that should be checked,cleaned, replaced as needed. Doing some reading in the SouthBend section at the "Practical Machinist" forum could help with idea's of whats inside/envolved with working on the spindle. Even though its probably not a South Bend lathe, its design will be close to the older lathes SouthBend made. Infact they have a older machinery section there (PM forum)that you could post pics of your lathe and maybe get some better input of the maker of the lathe.
Either way this is about as simple of a lathe design as there could be. It will make a great lathe if keep in shape, and be very usefull in about any shop.
Jess
GOD Bless, and prayers for all.