Recently, we introduced two sequences of polynomials (B n (x, y, z)) and (F n (x, y, z)), which unify many familiar polynomials related to Dowling lattices, such as the Bell polynomials, the Dowling polynomials, the ordered Bell polynomials, the r-Bell polynomials and the r-Dowling polynomials. In this paper, we show the asymptotic normality of coefficients of B n (x, y, z) and F n (x, y, z). As applications, we obtain the asymptotic normality of coefficients of some polynomials related to Dowling lattices in a unified approach.