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/N...