This lamp needed only 4 cracked pieces to be replaced. Here are two, marked in blue tape ..
And here are the other two, also marked with blue tape.
The first step is to score the cracked piece with a glass cutter (shown). Then the piece is repeatedly tapped with the metal end of the cutter to loosen the glass.
Here the glass is nearly all removed.
The adjacent piece also needs replacement, but for the time being, I left it in place.
In the process of removing the larger cracked piece, an adjacent smaller one loosed. Here I put it back in place after I applied new copper foil to its edges, and to the borders of the nearby pieces.
After the larger piece of glass was removed, I cleaned off the old solder and foil. Then I traced a pattern as shown.
Using the pattern, I cut a new piece of green glass. Here I'm using "groziers" to chunk out small pieces of glass along edges. This saves time at the grinder.
Then I apply copper foil along the edge of the replacement piece, as well as inside the borders of the dome where it will be soldered.
Now all three pieces have been replaced and soldered into place. This is the view from inside the dome.
Moving around to the other side of the lamp, I've removed the piece of cracked glass which extends up to the border.
After making a pattern, cutting new glass, and preparing it, I've replaced it into the lamp as shown.
Here I'm applying black patina to the solder.
Soldering and patina-ing is complete .. Next I'll wax the lamp for protection and shine.
Here is one side of the lamp, repaired and ready to be enjoyed again.
And here is the other side, repaired. Thanks so much Sandhya, for bringing me two lamps to repair for you!