Here is the "before" photo. The lamp was completely separated, top to bottom. The cracked pieces are marked with blue tape.
After assessing the damage, I formed my action plan for repairing it. First, I removed the existing foil and solder from the border up top where the cap belongs. Securing the cap back on was, to my mind, the best way to stabilize the dome.
I ringed the inside of the cap with new foil, and also added new foil to the inner border of the top of the dome. After applying liquid flux to the foil, I soldered the cap back in place, using generous amounts of solder for a secure bond.
With the cap in place, I decided to secure the bottom edge of the lamp, then work toward the middle. Here I've taped the lamp in place.
The bottom of the lamp had split completely, and the wire which supports the outer edge of the lamp had also separated. I added new copper foil to the length of the border to enable me to secure new wire to that edge. Then, working from the edge, I re-foiled and then soldered the lower glass pieces.
At this point, the lower edge is secure, as is the top, so I'm working my way through replacing the other cracked pieces. Note the two new glass pieces which have just been foiled, at the top near the cap.
Here's an outside view of the dome, with those pieces soldered in place and several more pieces intentionally removed.
The view from the inside of the lamp dome. I'm taping pieces in place and continuing with replacing the cracked pieces.
Here I've cut a new piece of glass and I'm trying it out for size. In many cases, even when a pattern is accurate, glass may be too small or too large for the space. In that case, I need to make adjustments. This piece will fine fine.
View from inside the dome. The piece shown is now in place.
Here's another piece I'm fitting in to the lamp.
Now I'm coming back to the border, where I've taped down a length of wire the same gauge as the original. This wire will be fluxed and then soldered onto the edge as shown, on top of the copper foil. This lends a great deal of strength and stability to the dome, and will help prevent future damage to the repaired areas.
In the course of doing repairs, as mentioned earlier, pieces which appeared to be fine also receive damage. This was the case here.
And another crack appeared adjacent to the one I was working on. I'd rather see them now, while I'm working, than later. So both the prior piece and this one were replaced. I had plenty of glass on hand to do the repairs.
Here are some of this lamp's pattern pieces. They say "out" as a tip to me to be sure that I cut the glass on the correct side to match the rest of the lamp.
After all of the cracked pieces are replaced, I'm soldering them, starting from the inside of the dome.
And after the lamp receives another cleaning, I apply "stained glass finishing compound" which is a light wax. This protects the patina and shines up the glass. And here's the repaired lamp!
The repaired view, from inside the dome ..