Abstract
An ideal I is a hereditary and additive family of subsets of positive integers N. In this paper, we will introduce the concept of generalized random n-normed space as an extension of random n-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence and L-ideal Cauchy for sequences of complex numbers in the generalized random n-norm. We introduce I-L-limit points and I-L-cluster points. Furthermore, Cauchy and I-L-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.