In this paper, we have introduced the concept of the set of rough I3-lacunary limit points for triple sequences in 2-normed spaces. We have established statistical convergence requirements associated with this set. Furthermore, we have introduced the idea of rough I3-lacunary statistical convergence for triple sequences. Additionally, we have demonstrated that this set of rough I3-lacunary limit points is both convex and closed within the context of a 2- normed space. We have also explored the relationships between a sequence’s rough I3-lacunary statistical cluster points
and its rough I3-lacunary statistical limit points in the same 2-normed space. Expanding upon the concept of triple sequence spaces, we have introduced the notion ofWijsman I3-Cesáro summability for triple sequences. In doing so, we have investigated the connections between Wijsman  strongly I3-Cesáro summability and Wijsman statistical I3-Cesáro summability. Furthermore, we have introduced the concepts of Wijsman rough strongly p-lacunary summability of order  and Wijsman rough lacunary statistical convergence of order  for triple sequences. These new concepts
have been subjected to a thorough examination to understand their characteristics, and we have explored potential connections between them. Additionally, we have investigated how these newly introduced concepts relate to existing notions in the literature.