Since the records exist, it doesn't seen worthwhile to make one's own Lang encyclopedia; plenty of accurate history seems to be there.
As for labels, I'm wondering if James Lang didn't just continue using the old Joseph Lang labels. Here are a James Lang matched pair SN 10411 & 10632....but the case has the Joseph Lang label.
http://heritageguns.co.uk/Lang%20SLE%20Pair/Lang%20SLE%20Pair%20Details.htm
This auction sold an allegedly original James Lang case with Label (no pics of the label). Might try to contact them though 6 years have passed:
https://s3-eu-west-1.amazonaws.com/ukauctioneers.com/pdf_catalogues/1565_with_images.pdf