Lineage fitness theory, developed here, aims to explain a sizeable portion of fitness-relevant acculturated behavior in humans in terms of a strategy adopted by lineage elders and ancestors according to which they maximize their inclusive fitness by generating and maintaining traditions that manipulate the psychology and behavior of their co-descendants. Lineage fitness theory includes the lineage fitness hypothesis, which is responsible for entailment of several novel predictions, and the lineage manipulation mechanism, which is responsible for causally explaining how elders and ancestors improve their fitness through promulgation of traditions that enhance co-descendant survival, increase welfare tradeoff ratio amongst distant co-descendants, and govern mating preferences and behaviors of co-descendants. Following presentation of the theory in Part A, a case study is developed in Part B in which the theory is applied to pre-historical and historical Han Chinese culture. Implications of lineage fitness theory on evolutionary psychology and cultural evolutionary science are addressed.