Mixed surfactant systems with strongly bound counterions show many interesting phases such as the random mesh phase consisting of a disordered array of defects (water-filled nanopores in the bilayers). The present study addresses the non-equilibrium phase transition of the random mesh phase under shear to an ordered mesh phase with a high degree of coherence between nanopores in three dimensions. In situ small-angle synchrotron X-ray study under different shear stress conditions shows sharp Bragg peaks in the X-ray diffraction, successfully indexed to the rhombohedral lattice with R3̅m space group symmetry. The ordered mesh phase shows isomorphic twinning and buckling at higher shear stress. Our experimental studies bring out rich non-equilibrium phase transitions in concentrated cationic surfactant systems with strongly bound counterions hitherto not well explored and provide motivation for a quantitative understanding.