Abstract : In this paper we introduce and study the lacunary strong Zweier sequence spaces $N_{\theta}^0[\mathcal{Z}],~~N_{\theta}[\mathcal{Z}]$ consisting of all sequences $x=(x_k)$ such that $(Zx)$ in the space $N_{\theta}$ and $N_{\theta}^0$ respectively, which is normed. Also, prove that $N_{\theta}^0[\mathcal{Z}],~~N_{\theta}[\mathcal{Z}]$ are linearly isomorphic to the space $N_{\theta}^0$ and $N_{\theta}$, respectively. And we study some connections between lacunary strong Zweier sequence and lacunary statistical Zweier convergence sequence.