The thermal conductivity k of the iron-arsenide superconductor LiFeAs (Tc ~ 18K) was measured in single crystals at temperatures down to T~50mK and in magnetic fields up to H=17T, very close to the upper critical field Hc2~18T. For both directions of the heat current, parallel and perpendicular to the tetragonal c-axis, a negligible residual linear term k/T is found as T ->0, revealing that there are no zero-energy quasiparticles in the superconducting state. The increase in k with magnetic field is the same for both current directions and it follows closely the dependence expected for an isotropic superconducting gap. There is no evidence of multi-band character, whereby the gap would be different on different Fermi-surface sheets. These findings show that the superconducting gap in LiFeAs is isotropic in 3D, without nodes or deep minima anywhere on the Fermi surface. Comparison with other iron-pnictide superconductors suggests that a nodeless isotropic gap is a common feature at optimal doping (maximal Tc).