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.