I have an old worn out SHOEI motorcycle helmet. It's time for a replacement, but it occurred to me that perhaps there is a place that refurbishes the things. It needs a new visor, but it also could use a new lining. Is this done, and is it economical?

Try www.redbaronbkk.com

They do some bits and bats that may help

Helmets age. The interior part in particular is specially made to protect the old bean. It must cushion but not rebound. By "made specially," I mean tested and approved by a manufacturer who then labels the helmet according to the standards for which it was built, if the design has passed the tests. To "refurbish" a helmet almost certainly means using an unsafe material or a material used in Thai helmets, which do not have ratings of STAR, Euro, Dot, or Snell. In short, you probably could buy a helmet at Carrefour for 400 baht and get as much protection. I don't know about the shell, but by itself, it would do no good.

Even a new helmet, once it has protected the rider in an incident, is risky to wear, as the saving portion has been compressed. Yours will have aged beyond safe margins, as you know.

The quick answer is "no". As mentioned above, it is the interior hard foam (similar to styrofoam/coffee cup material) that crushes at an engineered compression rate that protects your head. No one guts a helmet and replaces this foam. Max life on any helmet is 5 years. The interior hard foam degrades over time from ozone, petrol fumes, UV, etc. Toss the Shoei, go buy a new helmet. Moved to the Motorcycle forum, with a live link on CM remaining.

Buy a new one, because as you said it is an old worn out helmet.