Context. Planetary systems hold the imprint of the formation and of the evolution of planets especially at young ages, and in particular at the stage when the gas has dissipated leaving mostly secondary dust grains. The dynamical perturbation of planets in the dust distribution can be revealed with high-contrast imaging in a variety of structures. Aims. SPHERE, the high-contrast imaging device installed at the VLT, was designed to search for young giant planets in long period, but is also able to resolve fine details of planetary systems at the scale of astronomical units in the scattered-light regime. As a young and nearby star, NZ Lup was observed in the course of the SPHERE survey. A debris disk had been formerly identified with HST/NICMOS. Methods. We observed this system in the near-infrared with the camera in narrow and broad band filters and with the integral field spectrograph. High contrasts are achieved by the mean of pupil tracking combined with angular differential imaging algorithms. Results. The high angular resolution provided by SPHERE allows us to reveal a new feature in the disk which is interpreted as a superimposition of two belts of planetesimals located at stellocentric distances of ~85 and ~115 au, and with a mutual inclination of about 5°. Despite the very high inclination of the disk with respect to the line of sight, we conclude that the presence of a gap, that is, a void in the dust distribution between the belts, is likely. Conclusions. We discuss the implication of the existence of two belts and their relative inclination with respect to the presence of planets.