The lead oval in the center of the door has slipped down about 2 inches from the top. Can the molding be removed to access the lead portion? Also, can the lead insert be moved back in the correct position and will it stay? If this can be done, what is the procedure to accomplish this task?
My answer is a definite maybe! It's hard to tell without seeing this (post pictures!), but most inserts are held in place by molding which is attached to the door by pressure fit of the two sides of the molding (snapped together), or mechanically where the molding has plugs that cover screws which hold it together in the door. The entire assembly could also have originally been attached with an adhesive caulk like product, as well.
To start, I'd take the door off the hinges and try and figure out how the molding was originally attached to the door. If you can get the molding off - great. If not, perhaps you can realign the leaded glass insert and then use a clear adhesive caulk to seal it to the molding and the molding to the door. That should hold you a couple of years but it might eventually have to be repeated. If you can post pictures, I can try and be more specific on the answer.