Baby Lassiter was the storked baby of Columbus, Ohio.
It was unspecified whose house he was first left in, but, at one point, he ended up at the doorstep of the Lassiter family's home. Connor was seven and also already had a younger brother, so their parents weren't planning on having any more children. Figuring that no one saw them get storked, their father left the baby on their neighbor's doorstep.
The baby was since then transferred to someone else's porch again, and was continuously passed around the neighborhood, no one wanting a baby. Two weeks later, the baby was again left at the doorstep of the Lassiter family; this time, with jaundice. The infant was sick and in very bad condition, so when they brought him to the hospital, he died shortly afterwards.
Since the child legally 'belonged' to Lassiter family, they paid for the funeral, which all their neighbors—all the people who did not want the child and passed him around—attended and cried at like it was their baby that had died. He didn't have a name, and, since Connor's parents couldn't bear to give him one, he just became "Baby Lassiter".
This event greatly affected Connor and continued to haunt him even years after. This likely contributed partly to the resentment he has toward his parents, and his sympathy for storked and unwanted children. It was his memory that urged Connor to save Didi from the unwilling family she was storked in.