Recently, the notion of weighted lacunary statistical convergence is studied in a locally solid Riesz space for single sequences by Başarır and Konca [7]. In this work, we define and study weighted lacunary statistical $\tau$-convergence, weighted lacunary statistical $\tau$-boundedness of double sequences in locally solid Riesz spaces. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces and give some inclusion relations.