Molecular dynamics simulations of aqueous LiCl solution have been carried out over wide concentration (from 0.1 to 11.4 mol/kg) and temperature (from -30 to 110 degreesC) ranges. Three different interaction potentials are investigated: the recent Li+-water effective pair potential, derived from ab initio molecular dynamics simulations [Lyubartsev, A. P.; Laasonen, K.; Laaksonen, A. J. Chem. Phys. 2001, 114, 3120], as well as earlier potentials of Lennard-Jones type with two widely different sets of parameters [Dang, L. X.; J. Chem. Phys. 1992, 96, 6970 and Heinzinger, K.; Physica B 1985, 131, 196]. Hydration structure and residence times around Li+ are studied with focus on the still somewhat controversial issue of hydration structure: both tetrahedral and octahedral water coordination have been predicted from the experiments. Besides classical MD simulations, even complementary Car-Parrinello simulations were employed to investigate the stability of a possible six-coordinated hydration shell around lithium. Self-diffusion coefficients for lithium were calculated for Li+ from the simulations and compared to NMR spin-echo measurements. The new ab initio-based exponential Li+-H2O interaction potential appears to be robust giving the overall characteristic hydration properties in agreement with experiments. However, while it reproduces the radial distribution function (RDF) features from a recent neutron diffraction with isotopic substitution (NDIS) experiments with a well-pronounced tetrahedral water structure, the same experiment is interpreted to give octahedral water structure around lithium at the same concentrations and temperatures as were used in our simulations.