What a great score and great story! I called several powder coating places last year looking at painting a Mondia with similarly beautiful chrome lug work. None would take the job because they could not guarantee that the lugs would survive the baking process. That led me to a paint shop that gave me an astronomical quote and eventually someone who hand paints frames.
As others have suggested, I cleaned and waxed the frame and was actually quite happy with the results. So I kept it that way. I just did the same with an Atala Record Professional with a lot of patina. While you may opt to paint, I would be suspicious of any powder coating operation that says they can protect your lugs.