Picosecond lifetimes of medium spin states in Lu-165 were measured for the first time. The reaction used to populate the nucleus of interest was La-139(Si-30,4n)Lu-165 at a beam energy of 135 MeV. The beam was provided by the XTU-tandem accelerator of Laboratori Nazionali di Legnaro, Italy. By using the differential decay curve method, lifetimes of 19 states in four different rotational bands were obtained. Therefrom the B(E2) values and the transitional quadrupole moments were deduced. The obtained Q(t) for the different bands are compared with total Routhian surface (TRS) calculations and particle-rotor-model calculations. The TRS calculations predict different axial symmetric shapes for the bands built on the 9/2(-)[514], 9/2(+)[404], and 1/2(-)[541] configurations, with a gamma softness for the 9/2(-)[514] configuration. This band has also been studied using the particle-rotor model, the results of which, however, are consistent with a triaxial shape with a gamma value of -15(p).