We investigate the electrochemical stability of tetragonal, cubic, and doped Li7La3Zr2O12 (LLZO) in a Li battery by performing both energy level alignment across the Li-LLZO interface and grand-canonical phase analysis in unison. We employ density-functional theory (DFT) as well as GW many-body perturbation theory for more accurate electronic energy levels. We explicitly enumerate interface structures of minimal lattice mismatch, determine energy level alignment for each interface using the average electrostatic potential as the reference, and combine the results with canonical thermodynamic averaging. We further study the effects of Ta and Nb doping of LLZO systems in the effort to explain the limited electrochemical stability observed in experiments over extended periods of contact or during cycling. We show that, compared to the more expedient vacuum-slab model, direct level alignment through the interfaces can substantially sway the predicted stability margins against electron transfer. We show that regardless of doping, LLZO at nominal composition should be electrochemically stable against Li. However, we identify formation of intermediate electronic states in the bulk of doped LLZO during lithiation as an intrinsic source of instability of doped LLZO against Li in a battery setting. These states localize onto the dopant atoms and fall below the Li Fermi level, effectively allowing electrons to be admitted at a positive voltage. Electron transfer onto of the dopant atoms would ultimately lead to phase separation, completing reductive decomposition of LLZO. A holistic pathway from electron spillover to LLZO degradation is thus established.