It is always difficult to predict the temperament of a crossbreed, due to the fact that two or more breeds are blended resulting in the mixing of temperaments as well. With dogs that come from a tried and true bloodline, the temperament is easier to predict as responsible breeders have extensive knowledge about the dog's generational history, breed characteristics, and the predisposition of the breed. Of course this is not predictable 100% of the time, but for the most part, you know what you are getting. With a crossbred dog, it is always a crapshoot. The dog could present the temperament of one of the two breeds, or a combination of both.
This does not rule out the importance of training and the environment. In most cases training and consistency can help to mould the dog's character, change unwanted behaviours, and teach better social skills.
Your best bet would be to research the temperament of both the Great Pyrenees and the Labrador Retriever. Both breeds were developed for specific purposes, the Great Pyrenees to guard flocks of sheep and the Lab to retrieve birds and perform other water related jobs. The Great Pyrenees may prefer to stand guard in the back yard while the Lab may prefer to lie on the couch. The Lab will appreciate time at the lake, but perhaps the Great Pyrenees will prefer to stay dry. The Great Pyrenees is wary of strangers and may challenge other dogs while the Lab loves everybody. Either way, this new addition will require daily walks and possibly some off leash time whenever possible.
Before making any decisions spend time with the dog and get to know her. Ask the shelter staff and volunteers questions about her behaviour with a wide range of people, most importantly children. Trust your instincts. Don't rush into your decision, you may live happily ever after, or you may regret your choice.
Hope that helps.
Sincerely Zena & Zippy