In this talk, we present our work as part of the “Final Project Paper” course, mentored by dr. Russ Woodroofe. We study Brown’s definition of P(L, s), as well as propose a natural alternative that may be better-suited for non-atomic lattices. In this case, we obtain a general Dirichlet series expression for P(L, s), which need not be an ordinary Dirichlet series. We investigate general properties of P(L, s) and compute it on several examples of finite lattices, establishing connections with well-known identities. Furthermore, we investigate when P(L, s) is an ordinary Dirichlet series. Since P(C(G), s) is always such, we call such lattices coset-like. In this regard, we focus on partition lattices and 2-divisible partition lattices and show that they generally fail to be coset-like.