Many versions of Quantum Gravity foresee the breakdown, at the Planck scale, of two of the building blocks of the Standard Model of Particle Physics (SM): the Lorentz and the CPT symmetries. Direct observations at the Planck scale are not yet possible, however Physics beyond the SM could produce effects at low energies, for example in the neutrino sector. We discuss the presence of a Lorentz and CPT-violating double-beta decay mode in data from the Phase II of the GERDA experiment, located at LNGS in Italy