We have fabricated c-axis point contact junctions between high-quality LiFeAs single crystals and Pb or Au tips in order to study the nature of the superconducting order parameter of LiFeAs, one of the few stoichiometric iron-based superconductors. The observation of the Josephson current in c-axis junctions with a conventional s-wave superconductor as the counterelectrode indicates that the pairing symmetry in LiFeAs is not pure d-wave or pure spin-triplet p-wave. A superconducting gap is clearly observed in point contact Andreev reflection measurements performed on both Pb/LiFeAs and Au/LiFeAs junctions. The conductance spectra can be well described by the Blonder-Tinkham-Klapwijk model with a lifetime broadening term, resulting in a gap value of \approx 1.6 meV (2{\Delta}/kBTC \approx 2.2).