  Exact mechanisms of thermal conductivity in liquids are not well understood,
despite rich research history. A vibrational model of energy transfer in dense
simple liquids with soft pairwise interactions seems adequate to partially fill
this gap. The purpose of the present paper is to define its applicability
domain and to demonstrate how well it works within the identified applicability
domain in the important case of the Lennard-Jones model system. The existing
results from molecular dynamics simulations are used for this purpose.
Additionally, we show that a freezing density scaling approach represents a
very powerful tool to estimate the thermal conductivity coefficient across
essentially the entire gas-liquid region of the phase diagram, including
metastable regions. A simple practical expression serving this purpose is
proposed.
