The impact of Li doping on the temperature-induced phase transitions in silver niobates Ag1xLixNbO3 has been investigated using a combination of high-resolution powder neutron diffraction and synchrotron X-ray diffraction. Considering both the cell metric and distortions of the NbO6 octahedra, estimated by Rietveld refinements, it is shown that the sequence of temperature-induced phases in AgNbO3 is P2(1)am -> Pcam -> Cmcm -> P4/mbm -> Pm (3) over bar. This sequence is simpler than that proposed in earlier studies. Evidence is presented for a second-order JahnTeller distortion in the Pcam phase. At x > 0.05, Li doping favors the formation of a rhombohedral phase in space group R3c, and such samples display the temperature-induced sequence R3c -> Pbnm -> Cmcm -> P4/mbm -> Pm (3) over barm. Unusual volume changes associated with the phase transitions point to the potential importance of lattice matching in optimizing the properties of thin films of doped AgNbO3