It's really difficult to say from that pic, but it appears as if you have what is known as a "Fantasy" piece. That is, one that is styled in the old fashion, but is not old and was never produced back then.
The reason I say this, is because your lamp seems to be in it's original state, but it's not likely that there would be an oil lamp mounted on such a post as is the case on this table lamp, and table lamps were not synonymous with oil lamps.
If you'd like to send in close-up photos of the underside of the table platforms that would probably tell for sure. If you truly think that the basin of the lamp was mounted on that brass post aftermarket, send a clear photo of where they meet. That will tell us a lot.