The creep anisotropy of a duplex Mg-9Li-4Al-1Zn (LAZ941) alloy, possessing a lamellar microstructure with both geometric and mechanical heterogeneity, was systematically investigated. The minimum creep rate and fracture behavior were dependent on the geometric relationship between the tensile stress axis and the phase boundaries. Specifically, the creep resistance was superior when the stress axis was parallel to the phase boundaries compared to the perpendicular orientation. This anisotropy was found to originate from the distinct mechanical responses of the layered microstructure, which can be consistently explained by a composite theory. When loaded parallel to the phase boundaries, the hard and soft phases deform under an isostrain condition. As a result, the macroscopic creep behavior is strongly influenced by the more creep-resistant α phase, leading to a low creep rate and a stress exponent approaching that of the α phase. Conversely, when loaded perpendicular to the phase boundaries, the constituent phases deform under an isostress condition. This concentrates strain within the softer β phase, resulting in a high creep rate and a stress exponent approaching that of the β phase. These findings provide a foundational framework for the composite-theory-based design of materials possessing a lamellar structure.