Following the Green-Kubo formalism in linear response theory, the lattice thermal conductivity of solid argon is determined by using classical molecular dynamics simulation to calculate the heat current correlation function. Comparing the absolute conductivities obtained using the Lennard-Jones potential with experiments, we find the predicted results to uniformly underestimate the measurements in magnitude, whereas the calculated temperature dependence corresponds well with the data. The temporal behavior of the heat current autocorrelation function shows that while a single exponential decay description is appropriate at elevated temperatures, below the half of the Debye temperature, the heat current relaxation clearly consists of two stages, an initial rapid decay associated with local dynamics followed by a slower component associated with the dynamics of lattice vibrations (phonons).