This paper explores the concepts of (Formula presented.) -lacunary statistical limit points, (Formula presented.) -lacunary statistical cluster points, and (Formula presented.) -lacunary statistical Cauchy multiset sequences. Building upon previous work in the field, we investigate the relationships between (Formula presented.) -lacunary statistical convergence and (Formula presented.) -lacunary statistical convergence in multiset sequences. The findings contribute to a deeper understanding of the convergence behaviour of multiset sequences and provide new insights into the application of ideal convergence in this context.