It is supposed that diffusive reconstructive transitions usually take place under hydrostatic pressure or low stresses, and displacive reconstructive phase transitions easily occur at nonhydrostatic pressure. Here, by in-situ high pressure synchrotron X-ray diffraction and single-crystal Raman scattering studies on lithium aluminate at room temperature, we show that the reconstructive transition mechanism is dependent on the internal microscopic stresses rather than the macroscopic stresses. In this case, even hydrostatic pressure can favor the displacive transition if the compressibility of crystal is anisotropic. During hydrostatic compression, gamma-LiAlO2 transforms to delta-LiAlO2 at about 4GPa, which is much lower than that in previous nonhydrostatic experiments (above 9GPa). In the region where both phases coexist, there are enormous microscopic stresses stemming from the lattice mismatch, suggesting that this transition is displacive. Furthermore, the atomic picture is drawn with the help of the shear Raman modes. Published by AIP Publishing.