The nuclear potential energies of Lu isotopes with neutron number N=90−98 up to high spins are computed within the framework of the unpaired cranked Nilsson–Strutinsky method. The potential and the macroscopic Lublin–Strasbourg drop (LSD) energy-surface diagrams are analyzed in terms of quadrupole deformation and triaxiality parameter. The shape evolution of these isotopes with respect to angular momentum, as well as the neutron number is studied.