I have strong prey drive dogs too-Alaskan Malamutes-who cannot be trusted with my chickens or any smaller anmals. I keep them either on a leash or behind their fence, which is topped with a hot electric fence. The chickens are not allowed free range because they like to fly into the dog pens. Suicidal birds.
I also have a sweet, mild manered English Setter. She has, and will, take down a flying hen or roo. So far she hasn't killed it, just held it until I could get to her and liberate the poor bird, but I know the potential is there. A Lab would be the same way. A dog is a prey animal. Deep down inside they are still a wolf. You can't blame an animal for being itself and following what it has evolved to be.
My dogs are my heart and soul. The chickens are there to provide eggs for the dogs. I would never get rid of a dog for being a dog.