Dogs do love to dig. A few things I did with my kids is put there poop in the hole and cover it up. That seemed to help a lot. I also started to run them 5+ miles a day (you will have to start out with long walks). You will have to read up on how much a lab should be run. Mine are huskies and need to run that much.
I also put in a sand box and let the sprinklers hit it. They just love the wet sand. I used retaining wall blocks for the sand box. You can use anything from a old plastic summing pool or a reg kids sandbox. If you do use those items punch holes in the bottom so the water can drain. They do like it wet. They did stop digging my lawn up after I put one in.
I moved my garden to a location that wasn't in there fenced yard because of the onions. The little robbers also picked all my veggies and had them all over the lawn. It was easier for me not to have the problem with trying to keep them out of it.
Good luck with your puppy, I hope that some of these things will help.
Try to create a place for him to dig. Dogs, especially puppies, like to dig and create little nests. Also make sure he gets plenty of exercise...labs need tons of it! Definitely fence the garden if you can... :)
He's your friend,your partner,your defender,your dog.You're his life,his love,his leader. He will be faithful and true to the last beat of his heart.You owe it to him to be worthy of such devotion