In this paper, we propose to use a lattice reduction (LR) approach to enhance the performance of spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems using filter-bank multicarrier (FBMC) modulation. It is known that lattice-reduction-aided (LRA) MIMO receivers can achieve full spatial diversity. On the other hand, the presence of the intrinsic interference in FBMC is widely regarded as a factor that prevents the system from taking advantage of spatial diversity when combined with SM-MIMO. We will show that with an adequate adaptation to FBMC modulation, the LR approach can be performed in a straightforward manner. Simulation results show that an LRA equalizer allows an FBMC-MIMO system to benefit more from the available spatial diversity and offers an interesting performance gain compared to the existing solutions with reasonable complexity.