One of the best things about repairing vintage clothing is getting to examine the items so closely and learn from them. In this case, I took notes all long, and now have a pattern for making a really cool accessory that isn't exactly common these days.
The repairs needed were just to reattach the big lace where it had come loose and replace the little lace at the top which had disintegrated. I also made an extension piece for the collar, so that the jabot will go all the way around and close in the back. Since I wasn't actually making one, I don't have step-by-step construction pictures, but will share my measurements and my best guess as to how it would work.
collar: cotton, cut 2 strips, 16" or 17" x 2"
center placket: cotton, cut 2 strips, 5 1/2" x 1 3/4"
6" deep lace: 44" long
small 1/2" lace: 17"
1. collar - Lay the two strips together, and sew a 1/4" seam all around, leaving a space in the center of one long side to turn. Clip corners and turn.
2. placket - Lay the two strips together, and sew a 1/4" seam on both long sides and one short end. Clip corners and turn.
3. Press both pieces flat. Top stitch placket edges.
4. Insert open end of placket into the opening at the center of collar band. Top stitch edges of collar. The top stitching will also attach the placket to the collar.
5. Gather the big lace to 9". (Yes, gather 44" of lace down to 9". It needs to be a soft lace.)
6. Fold in the lace strip in half, like closing up a V, and sew a narrow seam to join the gathered edges together.
7. Stitch the lace seam to the center of the placket. This side will be the front.
8. Turn under raw edges of the lace at the top, and stitch across the collar band.
9. Stitch the small lace inside top edge of collar. Add snaps to close.
Here's the front: Gathered lace and its seam stitched to the placket. Top edge of lace turned and stitched to the collar.
Here's the back: The placket is only visible on the inside.
Look at how gorgeous this lace is!!! Because it's so very soft, it's able to take all the gathering, and hang in that wonderful swoop.