Joe T seems to think Jersey stole the baby and the phones. He was walking around carrying a baby at midnight. I am going to assume the baby was very quiet even though she was not clothed in 50 to 60 degree weather and being with a stranger.
That leaves the possibility that the child was deceased and "Jersey" was walking around the neighborhood with a almost naked dead baby for all to see. Okay, we can go with that. Now is this man sane or not sane at this point? I say a person doing this would have to be on the psychotic side/drunk/drugged. If "Jersey" was any of these, where would he leave the baby?
I have had the opportunity to read many files and talk to perps who did things like this but I can say they have been caught in almost every case because they leave tons of evidence in their wake. They don't think to wear gloves, it isn't pre-meditated and they drop the baby (I had one) out in the open (a baseball field in the one case).
If it wasn't him, I guess it was some other psychotic/drugee/drunk who got lucky and dropped her where nobody can find her....but that happening is slim to none.
A sharp person who broke in to steal Lisa would not concern themselves with three cell phones and turning all the lights on but making sure the baby's room stays dark. This is not the work of a skilled kidnapper.