If the item is heavy metal you can't do any harm removing the felt to view the bottom. Place the item on a "damp" towel and see if it will loosen the flet without harm to the felt or lamp.
Another great place to look is up at the neck of the lamp - near the bulb socket....any markings there?
Have seen some similar to this and they were from the 30's to 40's and there are repros out there.