Welcome to Forum williamwells 4401.
The LMS employment records are held at the Public Records Office at Kew. Could be a long job though as the LMS employed over 1,000,000 people.
There has also been a book published on research railway families.
http://webp1.mimas.ac.uk/~zzaascs/mrsoc/gene.html
This link to the Midland Railway Society might be helpful.
Best wishes,
John H-T.