In this chapter, we turn our attention to a more specialized situation. Rather than continuing to study connection matrices for general poset filtered chain complexes, we now consider the setting of Lefschetz complexes. Their definition and basic properties have already been recalled earlier in the book, and therefore this chapter focuses on the introduction of acyclic partitions in Lefschetz complexes, as well as their associated connection matrices. We then concentrate on the fundamental properties of a special case, the so-called singleton partition, and end the chapter with a discussion of refinements.