It is very hard to make any sort of credible argument that the African slave trade saved lives. There have been those who have tried to argue that it did, but they were generally people who had an agenda. They wanted to “prove” that slavery and the slave trade were not really such bad things. Their arguments have generally been discounted and not given much credence.
The most common argument of this sort holds that the Africans who were sold as slaves were people who had already been defeated in war. The idea is that, if these people had not been enslaved, they would simply have been killed. In this way, the Europeans (it is claimed) saved them by enslaving them. Historians, however, do not take this idea seriously.
Thus, the idea that the slave trade actually saved lives is not really taken seriously by any reputable scholars.