Yes and no... you have to remember that dachshund are VERY finicky and that labs are generally loving and care-free.
A dachshund often requires a special diet because they have sensitive stomachs and skin. They also should not be allowed to jump on and off furniture or climb stairs because this can cause severe and irreversible damage to their elongated spines.My dachshund is about 3 months old and is fairly spoiled, but he is also well-trained and disciplined. He already knows sit, down (lay down), off, speak, fetch, and drop it. (Sorry had to brag a bit).
However, your lab puppy should get some special attention too. Puppies especially need a lot of extra care and training. They too have sensitive stomachs.
Puppy time is make it or break it time. Your lab puppy will feel ignored and pushed away, much like a wolf who is shunned from a pack. Labs are very friendly and "pack" oriented. Your puppy may learn to resent the little wiener and be aggressive toward it.
Labs are much larger than dachshunds. This could cause BIG problems.