Hello Kara - welcome from me too

Can I ask where you got Robert's father's name?
Certainly the Robert birth reg. you found looks likely, there doesn't seem to be another born then in Lincolnshire. However, I see that in 1861 census both parents of that Robert were away from home

In 1871 that Robert seems to be in Yorkshire as a chemists and druggist aprentice, but the other two siblings from 1861 are home, with parents Michael and Elizabeth

This may not therefore be the one
