Hi. I'd like to know about State Lady in this context.
Mrs. Garret, otherwise known as the State Lady, comes to the farm every month.
(the farm here is a group home) She also visits his mother now and then.
(his mother is in prison now.)
Government workers are sometimes referred to as "people from the State". They are public service employees so they work for "the State", not for a private company.
In one of my favourite films, a character says something to the effect of "If you do that, the State guys will be round here so fast it'll make your head spin". The character is the older brother of three, their parents are dead and he is the guardian of the two younger brothers. He is worried that if they do anything to bring themselves to the attention of the authorities, someone from "the State" will come to the house and take the younger children into the care of social services.
In your example, the woman is "the lady who works for the State" and has come to be known as "the State Lady".
Bhaisahab is definitely on the right track, if not completely correct.
The words "group home", "mother", and "prison" make me think that The State Lady is an employee of the State's Family Services Administration (or some similar name).