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