In [18] has been proved some inequalities related to the rate of LP approximation by Ceshro means of the quadratic partial sums of double Vilenkin-Fourier series of functions from LP. These inequalities imply sufficient conditions which provide convergence in the norm of Ceshro means of the quadratic partial sums of double Vilenkin-Fourier series in terms of modulus of continuity. In this paper there is proved that these results are sharp in a certain sense.