Old shotguns oft have bbbls made of Damascus or twist steel. Steel and iron rids were heated till red,and forged around a mandrell to make the bbl. Unfortunately all the lines where the rods joined are susceptable to rust and weakness over a long time. Remove the forearm and see if there's any sign of lines, etc.
Some older Ithaca doubles shot themselves loose,and the design wasn't great for retightening. However, I'd get a second opinion from a good smith,and light skeet loads might be OK for an occasional shoot.
Also, modern shells are 2 3/4", while older guns may be chambered for a shorter shell, I think they used 2 1/16 for a 16 gauge. This needs to be checked before shooting. Using too long a shell boots pressures way up.
If the gun is usable, shoot it and enjoy. Most of those old doubles handle very well indeed...