The precise manipulation of magnetic anisotropy in spintronic systems exhibits revolutionary potential for next-generation technologies. However, achieving deterministic control at the atomic scale faces critical bottlenecks due to the intricate interplay among spin-orbit coupling, interfacial symmetry breaking, and thermal fluctuations. Here, based on first-principles calculations, we demonstrate effective the control of the easy magnetization axis for the LaBr2 monolayer by using strain engineering. The result shows that the biaxial compressive strain induces a fundamental transition of the easy magnetization axis from in-plane (xy plane) to out-of-plane (z axis). This change in easy magnetization axis stems from the strain-modulated orbital coupling between occupied and unoccupied dxy/dx2-y2 orbital states in La atom, which alters the energy splitting between competing magnetic anisotropy configurations. Our findings establish a viable pathway for engineering magnetic anisotropy in two-dimensional systems through lattice deformation, enabling potential applications in strain-controlled spintronic devices.