The reason we can add milk to goat milk soap without it going bad is because soap goes through a chemical reaction called saponification. This reaction takes the inputs and produces soap and glycerin as the outputs. The properties of the milk are in the soap, but it's no longer milk, so it doesn't spoil or grow bacteria. Unfortunately, lip balms and lotions do not undergo this same reaction.
I'm regularly asked if our goat milk soap will be better for someone's skin than the soap they are currently using. I'm a bit biased, but my answer is usually a laughing, "Of course!" I then qualify it to say that everyone's skin is different and I can't predict how their skin will react to our goat milk soap. But I do know that many other soaps and detergents are filled with chemicals that we avoid.