What is strange in this story is the involvement of the father.
IF Lillian had just been a young girl having an illegitimate child with no support, that she then abandons,one wouldnt expect the father to be such a feature. Unusual for him to turn up months later and accept responsibility.
It seems he must have known about the baby all along, known of its birth, but not registered it at the time, been in touch enough to know the facts, and for some reason something prompted him to register it some months later - and thus admitting paternity in writing on the birth cert. And then taking financial responsibility for the child.
He was either just a very responsible person, or he had enough involvement in the early days of the baby's life to have fully accepted his position. But why, then didnt he register the birth earlier?
I wonder if another possible scenario was that Lillian was from a well to do family, sent away to have this baby and then maybe married off to someone else? No evidence - just another idea to throw in the pot!
What else do we know about Alexander Harvey Lloyd? Occupation, did he marry, death, did he leave a will, etc etc.