We're told the LAPD is seriously looking at the possibility the shooter/thieves knew the dogs were owned by Gaga, and the video obtained by TMZ more than supports that theory.

If you look closely, the car that comes upon dog walker Ryan Fischer clearly was headed for him. The car stops and two people immediately jump out and attack the dog walker. There's no way they would have instantly known these dogs were a valuable breed ... they're small and it was dark outside. The dogs could have easily been rescues, mixed breeds, a less valuable breed ... fact is, these criminals knew.

What's more ... our law enforcement sources tell us, Ryan Fischer told numerous people in the neighborhood he was walking Gaga's dogs, so lots of people knew.

From what we know, this was supposed to be a short walk -- 10 PM at night, so the dogs could go poop and pee. It's not like the robbers were able to follow Ryan a long distance ... if they were indeed targeting Gaga's dogs, they could have scoped him out in the days before to determine his walking schedule.

As for the $500,000 ransom Gaga is offering ... sources with direct knowledge tell TMZ no one has been in touch with the singer or her reps so far demanding payment.