In this study, we explore the concept of lacunary Iσ-convergence of sequences and analyze the relationships between this new convergence concept and the notions of lacunary invariant summability, lacunary strongly s-invariant summability, and lacunary σ-statistical convergence, all of which are defined within quaternion-valued generalized metric spaces. Additionally, our paper aims to introduce the concepts of lacunary Iσ∗-convergence in quaternion-valued generalized metric spaces. We then establish the equivalence between lacunary Iσ-convergence and lacunary Iσ∗-convergence by providing the definition of property (AP). Furthermore,we introduce lacunary Iσ-Cauchy and lacunary Iσ∗-Cauchy sequences, adapting classical theorems to quaternion-valued generalized metric spaces.