The influence of the polymeric ionic liquid (PIL) Poly(diallyldimethylammonium bis(trifluoromethylsulfonyl) imide) (PDADMATFSI) on the lithium dynamics was investigated in a ternary gel polymer electrolyte consisting of PDADMATFSI as stabilizing polymer, ionic liquid (1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl) imide, P14TFSI) and lithium salt (lithium bis(trifluoromethylsulfonyl) imide, LiTFSI). The diffusion coefficient of the lithium ions is investigated by pulsed-field-gradient NMR, the conductivity of the electrolyte is determined by impedance spectroscopy. The local lithium dynamics is characterized by 7Li spin lattice relaxation rates (R1). The relaxation rates are well described by Blombergen-Purcell-Pound (BPP) theory at all polymer concentrations (up to 45mol%), implying that the Li dynamics is governed by one single motional mode. Interestingly, activation energies for this motion decrease from 20kJ/mol to 15kJ/mol with increasing polymer content and are independent on the salt content. We thus conclude that the polymer is interacting with the anion coordination shell, which is accompanied by a very beneficial effect on the local lithium dynamics, as the polymer PDADMATFSI reduces the Li-TFSI interactions. This result is promising for further investigations for potential use of PDADMATFSI-containing gels as electrolytes in energy storage devices.