Theories

Since it was common practice for orphaned babies to be named after an attending doctor and one of the attending doctors with Lilian was named George Smith, this could be where George got his name.
The child would be 50 years old this year (2017) and this is approximately George's age.
The LFoA Facebook page tells us that George came to them in 1998 and had a background in psychology and psychopharmacology but no degree was listed
If George went to college for a several years and then started to work for LFoA around age 30 that would make him around 50 years old this year (2017)
Dr. Richter, Lloyd McGowan's doctor (who was in the same facility as Lilian Grayson and accused of murdering her), sent George a letter thanking him for "taking an interest" in acquiring Lloyd and also Dr. Richter expressed his relief at "having him away from me" and "longing for a simpler life"
So it was a great burden having Lloyd all these years. Was that because Lloyd knew something he shouldn't have? Possibly witnessed the attack/rape of Lilian and this explains why Lloyd attacked the custodian, Robert Zykewski (see Robert Zykewski theory).
George Madson has an unusual interest in acquiring Lloyd and wants to take him "off his medicine to see what he has to say, if anything". Is he wanting to find out information that Lloyd knows about his Mother?
He then also acquires John William James which leads to the JWJ theory (SPOILER ALERT FROM BOX 3 FOR THIS THEORY)