If it's not been done yet, I'd sand it with a fine grit. Then tack cloth it. Then spray with a mist from water bottle and wait 10 minutes and sand it again. The water brings up all the little shreds the sand paper didn't get the first time. Then tack again. Then either spray or paint on a protective clear finish. Lots of them out there.
This is a real cute table that will be a conversation piece for a long time. I think it'll be nice with a big, black bottomed lamp on it.