NO!  A dog can survive on cat food but a cat cannot survive on dog
food.   Cat food contains ingredients that are not required by dogs.
I am hopeful one of the experts on cat nutrition will give you more
information.

I once had a cat like this, we used to let him eat dried dog food until I
learnt it wasn't good enough for him, so we started feeding him in a
different room, he starved for a week before he started eating dried cat
food!  I suggest use half and half to start off with, then gradually put
less and less dog food in his bowl.

Cat food is too rich for a dog, it will make them fat!

You should probably start feeding the labs and cat separately. We had a cat
like this as well, who wouldn't eat cat food... until we let the dog eat a
few kibbles of the cat food, as if to demonstrate that this stuff was just
as tasty. From then on, cats and dogs were fed separately. The dogs are fed
twice a day, enough to maintain proper weight but not so much that they'll
leave some in the bowl for the cats to get at, and the cat dishes are set in
a spot the dogs can't reach. If you have questions about the varying
nutritional requirements for cats and dogs, you can post the questions on
alt.med.veterinary.

Cats require specific nutrient that are not present in dog food to
adequate amounts. You must wean your cat off dog food. You may have to
shut your cat in another room and feed it at mealtimes, or mix the
dog/cat food and gradually alter the ratio.

Other than this, it's hilarious to have a cat who thinks it's a dog.
Does your cat fetch? Most cats, if you toss a ball for the cat to
retrieve, the cat will watch the ball roll away, look at you, and say,
"And...?"