She Lives in My Lap (feat. Rosario Dawson)

I think that u are right to an extent about the theory about her being in his lap as a pet is... But more thoroughly, It is about her coming and going. She is not physically with him, but he holds her dear to him. He carries her close to him wherever he goes. Metephorically speaking its like he cradles her as you would a pet even though she is not physically present