In this paper, by introducing the harmonic complex Lichtenberg sequence, we extend the classical complex Lichtenberg sequence through the incorporation of the harmonic number properties. The generating function plays a central role in establishing the analytical structure of the sequence, enabling the derivation of the closed-form expressions. This new sequence is rigorously defined using its generating function, from which we derive a determinantal formula for the complex Lichtenberg number. Furthermore, by applying the discrete difference operator, we develop a summation identity that characterizes the behavior of the harmonic complex Lichtenberg numbers, offering insight into their recursive and additive properties. In addition, we explore the matrix implications of the harmonic complex Lichtenberg sequence by constructing a special max matrix, whose elements are composed of these numbers. For this matrix, we derive explicit expressions for both its determinant and permanent, which provide critical information about the matrix's structural and its algebraic properties. These results contribute to a deeper understanding of the interplay between the number sequences and matrix theory. To support the theoretical findings, we include two detailed numerical examples that illustrate the practical computation of the determinant and permanent, thereby validating the correctness and applicability of our proposed formulas.