A room-temperature ionic liquid (RTIL) of a quaternary ammonium cation having an ether chain, N,N-diethyl-N-methyl-N-(2-methoxyethyl)ammonium bis(trifluoromethylsulfonyl)amide (DEME-TFSA), is a candidate for use as an electrolyte of lithium secondary batteries. In this study, the electrochemical ionic conductivity, a, of the neat DEME-TFSA and DEME-TFSA-Li doped with five different concentrations of lithium salt (LiTFSA) was measured and correlated with NMR measurements of the diffusion coefficients D and the spin-lattice relaxation times T, of the individual components DEME (H-1), TFSA (F-19), and lithium ion (Li-7). The ion conduction of charged ions can be activated with less thermal energy than ion diffusion which contains a contribution from paired ions in DEME-TFSA. In the doped DEME-TFSA-Li samples, the a and D values decreased with increasing salt concentration, and within the same sample generally D-Li < D-TFSA < D-DEME except for the sample having the lowest salt concentration at low temperatures. Since plots of the temperature dependence of T-1 of the H-1 and Li-7 resonances showed T, minima, the correlation times tau(c)(H) and tau(c)(Li) were calculated for reorientational motions of DEME and the lithium jump, respectively. At the same temperature, tau(c)(Li) is longer than tau(c)(H), suggesting that the molecular motion of DEME occurs more rapidly than the lithium jump. Combining the D-Li and tau(c)(Li), averaged distances for the lithium jump were estimated.