Energy levels of 30 low-lying states of Lu2+ and allowed electric-dipole matrix elements between these states are evaluated using a relativistic all-order method in which all single, double, and partial triple excitations of Dirac-Fock wave functions are included to all orders of perturbation theory. Matrix elements are critically evaluated for their accuracy and recommended values of the matrix elements are given together with uncertainty estimates. Line strengths, transition rates, and lifetimes of the metastable 5d(3/2) and 5d(5/2) states are calculated. Recommended values are given for static polarizabilities of the 6s, 5d, and 6p states and tensor polarizabilities of the 5d and 6p(3/2) states. Uncertainties of the polarizability values are estimated in all cases. The blackbody radiation shift of the 6s(1/2)-5d(5/2) transition frequency of the Lu2+ ion is calculated with the aid of the recommended scalar polarizabilities of the 6s(1/2) and 5d(5/2) states. Finally, A and B hyperfine constants are determined for states of Lu-175(2+) with n <= 9. This work provides recommended values of transition matrix elements, polarizabilities, and hyperfine constants of Lu2+, critically evaluated for accuracy, for benchmark tests of high-precision theoretical methodology and planning of future experiments.