In this paper we enunciate and rigorously demonstrate a new lemma that, based on a previously proposed theorem, proves the identifiability of leverage points in state estimation with specific reference to the Least Absolute Value (LAV) estimator. In this context, we also propose an algorithm for the leverage point identification in LAV estimators whose performance is validated by means of extensive numerical simulations and compared against the well-known approach of Projection Statistics (PS). The obtained results confirm that the proposed method outperforms PS and represents a significant enhancement for LAV-based state estimators as it correctly identifies all the leverage points in the measurement set.