Abstract
In this paper, we introduce the concepts of lacunary statistical tau-convergence, lacunary statistical tau-bounded and lacunary statistical tau-Cauchy for double sequences by using the double lacunary density in the framework of locally solid Riesz spaces. We also introduce the notion of S-(theta) over bar*(tau)-convergence of double sequences in this setup which seems to be a quite new and interesting idea and prove some interesting results related to these notions.