In 1881 Lydia is with parents Thomas and Elizabeth, along with siblings Emliy (1856 ) and Thomas (1854), so there are other siblings after Hannah before Lydia - of course there may be more who have left home.
RG11 1770 68 34
Have you got the family in 1871, 61, 51 etc?
I'd ascertain a few Facts before making assumptions about Lydia's parentage.
With family history anything is possible, but assumptions are extremely dangerous, as it is easy to assume the wrong anything!
Better to establish facts - even if it means forking out on certificates, searching beyond the internet etc.
just about to press 'post', and see you have posted and are going to get cert!! Good for you. I'll post anyway!