The thermal conductivity κ of the iron-arsenide superconductor LiFeAs (T_c 18 K) was measured in single crystals at temperatures down to T50 mK and in magnetic fields up to H=17 T, very close to the upper critical field H_c218 T. For both directions of the heat current, parallel and perpendicular to the tetragonal c axis, a negligible residual linear term κ/T is found as T→0, showing that there are no zero-energy quasiparticles in the superconducting state. The increase in κ with magnetic field is the same for both current directions and it follows the dependence expected for an isotropic superconducting gap. These findings show that the superconducting gap in LiFeAs is isotropic in 3D, without nodes or deep minima anywhere on the Fermi surface. We discuss how this behavior of the thermal conductivity may be reconciled with the multiband character of superconductivity in LiFeAs inferred from other measurements. Comparison with other iron-pnictide superconductors suggests that a nodeless isotropic gap is a common feature at optimal doping (maximal T_c).