Im going to say this just as a stupid theory.
I think lilith is part of a rich family that had relations with the MC parents, after they died she saw the kid being alone and wanted to help him but her family refused. Why take care of a child with no "relation" to the family? So she escaped and decided to still help using the savings that she had for the food and to pay the mansion. Now being the maid of the kid, she hides the fact that she is rich just to avoid the MC feeling guilty of making her work as a maid. She's going to stay with him untill he's old enough to use the saving his dead parents left him