You've got good taste, the Radius Dining Table in Oak has built quite a reputation as a design classic. It was originally spray lacquered, which was only ever going to last about eight or ten years before looking rough, and once it first starts to go it will then deteriorate pretty quickly.
You've got a dilemma in that, unlike most used furniture, it's not totally valueless. But preserving the value means putting it out to a professional for respraying to retain originality, that won't be cheap for a good job.
Your other option is sanding and scraping out the lacquer (about four to eight hours hard graft) and then refinishing yourself. Personally I'd go with Osmo, satin if you want to replicate the original, or matt if you want to be on trend. It's a hard wearing finish that even resists red wine as long as any spills are mopped up quickly, but the truth is most finishes apart from two packs will struggle under the assault course that is a family dining table. The advantage of Osmo though is that it's fairly easy to refresh or replace the finish every few years.
Good luck!
