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In the [3] is proven that sequence  uniformly statistically converges to L if and only if it there is a subset A of the set  uniform density zero and subsequence  defined by,  for  converges to L, in the Pringsheim’s sense. In this paper, it is proven that analog is valid and for lacunary uniformly statistical convergence. Double sequence  lacunary uniformly statistically converges to L if and only if it there is a subset A of the set  lacunary uniform density zero and subsequence  defined by,  for  converges to L, in the Pringsheim’s sense. The subsequence  lacunary uniformly statistically converges to L if and only if it there is a subset A of the set  lacunary uniform density zero and subsequence  defined by,  for  such that

multiple sequences, uniform statistical convergence.