Sorry about delay. No known connection but use of Lydia in both families may be significant.
My Lydia was GWR employee at Wooburn, Bucks where no doubt she met her husband who also worked for GWR. They married there, but moved back to his home town of Leamington Spa where they brought up a family.
The name is persistent too. 157 years after my Lydia was born, my aunt survives with the second name Lydia. And I also have second cousin called Lydia with this ancestry who is slightly younger and may still be living in Birmingham UK but we have lost touch.