Ok. There are multiple solutions.
1) If you want to leave your dog outside and he digs, you need to give him more exercise. Especially since he's a lab. The more bored he is, the more he digs. The more tired he is from exercise, the less he digs.
2) If you are going to leave him in, crate him and put a pee pad in the crate. Most vets have them. They are very absorbant.
3)You could contain him where there is no carpet in your house, that way it is easy to clean.
The best idea I think is to crate him and if he pees, then you can just toss the pee pad or clean the towels.
Or you could hire a local teen to let him out every couple hours. It just depends if you have the money to do that.