Hi Jonathan,
Welcome on the forum.
Your Jaeger-LeCoultre is indeed a beautiful oldtimer. It comes probably from the 40s or 50s looking at its calibre.
You can ask directly Jaeger-LeCoultre on their website
www.jaeger-lecoultre.com
Click on "Historical collection"
Then you can give the serial numbers we see on the pics, join a pic of the watch ( front pic would be better) and they will come back to you with the best information they can find.
Please let us know.
Cheers
Dje