You probably have a serviceable lathe.
In the 80s a buddy and I built our shop inventories by buying excess school shop equipment in closed bid county auctions every 6 months. Since they were phasing out school shops some good machine were in the lots.
We would fix up and sell some pieces and keep others. Tried to sell enough to make the machines we kept free.
We got Lathes with various name plates that looked real similar. J-line, atlas, delta, Rockwell.
A couple things I noticed with yours .
The banjo has either had a major repair or it may be a homemade replacement.
View attachment 44000
The banjo usually would have been a cast iron piece with no welds.
The two holes probably held the maker plate
View attachment 44001.
Not lucky enough to find it in one of the drawers.
There appears to be quite a tilt in the motor Mount.
View attachment 44002
The pulley looks to be at an angle to the belt from the tilt in the motor Mount.
Probably runs ok with A little added noise.
If you can square the motor Mount hinge it would run a bit smoother and quieter.