A few two-dimensional (2D) magnets have an intrinsic easy axis, which is essential for long–range magnetic ordering required for applications. Here, we show that in the absence of external magnetic fields, uniaxial strains can stabilize long–range ferromagnetic ordering in a 2D electrene, LaBr₂, by effectively changing its magnetic anisotropy from the original easy plane to an easy axis. Importantly, such manipulations do not affect the unique properties of its magnetic anionic electrons. The strain-dependent magnetic anisotropy is further understood by the Bruno's model. Monte Carlo simulations directly show an absence of collective magnetism in the pristine monolayer of LaBr₂, but the emergence of long–range magnetic ordering with high Curie temperatures when uniaxial strains were applied. Our results pave way to utilize 2D magnetic materials with interesting properties in the absence of magnetic anisotropy for practical applications.