The Laplacian matrix of a simple graph can be used as the Hamiltonian in Schrodinger's Equation. The resulting trajectory is the (continuous-time) Laplacian quantum walk. Laplacian fractional revival (LaFR) occurs when the Laplacian quantum walk becomes direct-sum decomposable with a 2-dimensional component. This phenomenon has been studied for the adjacency matrix as Hamiltonian and is of importance to quantum computation. In joint work with Ada Chan, Mengzhen Liu, Bobae Johnson, Malena Schmidt, and Harmony Zhan, we develop the theory of LaFR and characterize its occurrence and timing using the spectral decomposition of the Laplacian matrix. This leads to a polynomial-time algorithm to compute LaFR's occurrence and timing on a given graph. We then proceed to prove the non-occurrence of LaFR on trees with 3 or more vertices, as well as classify LaFR on all graphs with a prime number of vertices.