We study dipolar relaxation of a chromium Bose-Einstein condensate loaded into a three-dimensional (3D) optical lattice. We observe dipolar relaxation resonances when the magnetic energy released during the inelastic collision matches an excitation towards higher-energy bands. Spectroscopy of these resonances for two orientations of the magnetic field provides a 3D band spectroscopy of the lattice. The narrowest resonance is registered for the lowest excitation energy. Its line shape is sensitive to the on-site interaction energy. We use such sensitivity to probe number squeezing in a Mott insulator. Quantum dipolar gases have attracted much attention in recent years [1][2][3]. Following the seminal studies of Cr BoseEinstein condensates (BECs) [4][5][6][7] and the recent production of Er [8] and Dy [9,10] quantum gases, it is natural to study dipolar gases confined in optical lattices. Dipolar gases in lattices provide an ideal playground for studying quantum phase transitions in a system with long-range interactions. The unique properties of dipole-dipole interactions (DDIs) present direct similarities with the Heisenberg model of quantum magnetism [11][12][13][14] and lead to novel quantum phases displaying possible long-range ordering in lattices [15][16][17]. The nonlinear coupling between spin and orbital degrees of freedom provided by dipolar interactions [18][19][20][21][22][23] is particularly interesting. Although at large magnetic field, this coupling leads to fast dipolar relaxation losses for atoms in excited spin states [24], we have recently demonstrated that working at low magnetic field enables the study of multicomponent quantum gases with free magnetization [25,26]. Here we extend this research to include dipolar particles trapped in optical lattices and directly observe discrete, atom-number-dependent coupling between spin and orbital degrees of freedom.We study the magnetization dynamics of 52 Cr atoms loaded in a deep three-dimensional (3D) optical lattice. Under our experimental conditions, we produce a Mott insulator state with a core of two particles per site [27,28]. Compared to our previous results in two-dimensional (2D) optical lattices [23], the 3D confinement allows us to reach a new regime, where on-site dipolar relaxation is inhibited unless the released magnetic energy matches a lattice band excitation: dipolar relaxation is a resonant process. The interplay between the anisotropies of dipolar interaction and of lattice sites leads to a resonance spectrum which depends on the magnetic-field orientation. Measuring demagnetization as a function of the magnetic field for two orientations allows for spectroscopy of the 3D lattice band structure. We operate in an asymmetric 3D lattice such that the narrowest resonance is found to be sensitive to the on-site atom-number distribution and reveals the number-squeezed distribution of the Mott state. Changing our experimental conditions, we prepare sites containing three atoms. Spin-orbit coupling DDI then produces three-body states that a...