It's not as simple as all that. The child's father was still alive at the time. He probably would have been killed by the enraged husband.
Also, the welfare of the child was a concern to the mother. Lucius is a good man, but he is still a product of his time. The wife even had to go so far as tell him the the child was blameless.
I wonder if Pullo will ever tell Vorenus he knew about it, and that he killed little Lucius' father.
If that were true, she would not have killed herself and left him parentless.
Yes, yes, I know it's just a show, but what kind of mother leaves her children in such a way?
And Vorenus will probably latch on to the boy next season, as he is the last born of his wife, whom he loved very much.