The idea of lacunary statistical convergence sequences, which is a development of statistical convergence, is examined and expanded in this study on L − fuzzy normed spaces, which is a generalization of fuzzy spaces. On L − fuzzy normed spaces, the definitions of lacunary statistical Cauchy and completeness, as well as associated theorems, are provided. The link between lacunary statistical Cauchyness and lacunary statistical boundedness with regard to L − fuzzy norm is also shown.