This study reports on the optimization of garnet-type Li-ion conducting Li5La3Ta2O12 (LLTaO) solid electrolyte thin film growth by CO2-laser assisted chemical vapor deposition (LA-CVD) and the films' detailed structural as well as electrochemical characterization. By adapting the LA-CVD process parameters, high quality LLTaO films with tailored microstructures are successfully grown, which allows to correlate the films' microstructure and phase composition with their electrochemical performance. Explicitly, the influence of grain boundaries on the ionic conductivity is studied, and possible strategies to lower the grain boundary resistance are given. As deposited LLTaO films show a total ionic conductivity of 7.8.10(-6) S.CM-1 at 298 K (activation energy of 0.66 eV). By applying a post-annealing treatment the total ionic conductivity is improved up to 3.8.10 S.CM-1 at 298 K (activation energy of 0.52 eV). This is among the highest ionic conductivities reported for Li-ion conducting garnet-type thin films so far. A better suitability of garnet-type Li5La3Ta2O12 films for fundamental research as well as for application in all-solid-state thin film lithium ion batteries compared to commonly investigated Li7La3Zr2O12 films is proposed and discussed.