For a simple graph \( G \) with \( n \) vertices, \( m \) edges, and Laplacian eigenvalues \( \mu_1, \ldots, \mu_n \), the Laplacian energy \( LE(G) \) is defined as \( LE(G)=\sum_{k=1}^n| \mu_k-\frac{2m}{n} | \). In this paper, we derive an upper bound for the variation in Laplacian energy resulting from a removal of a vertex and characterize the graphs that attain this bound. Furthermore, we define the local Laplacian energy of a graph and establish its relationship with the Laplacian energy of the graph.