Investigating the concepts of Nörlund I2-lacunary statistical convergence and extremely intuitionistic Nörlund I2-lacunary convergence of double sequence in intuitionistic fuzzy normed spaces (IFNS) is the goal of this article. Then, we introduce the concepts of Nörlund strongly I2 *}-lacunary convergence, Nörlund strongly I2-lacunary Cauchy, and Nörlund strongly I2 *}-lacunary Cauchy double sequences in IFNS and get astounding results.