Abstract: This paper is a study on Complex integrable lattice functions and μ-free lattices. It initiates the concepts of complex integrable lattice function, positive and negative separations of μ and establishes the separation properties of complex integrable lattice functions. Also it introduce the concepts of free lattice, μ-free lattice and demonstrate that μ is a measure on β, μ is a free lattice in β, β is a μ-free lattice of σ (L). Also it was defined the concept almost free lattice and finally confirm that every almost free lattice is a complex integrable lattice function and a σ-additive.