An investigation has been carried out into the effectiveness of using symplectic/operator splitting generated algorithms for the evaluation of transport coefficients in Lennard-Jones fluids. Equilibrium molecular dynamics is used to revisit the Green-Kubo calculation of these transport coefficients through integration of the appropriate correlation functions. In particular, an extensive series of equilibrium molecular dynamic simulations have been performed to investigate the accuracy, stability and efficiency of second-order explicit symplectic integrators: position Verlet, velocity Verlet, and the McLauchlan-Atela algorithms. Comparisons are made to nonsymplectic integrators that include the fourth-order Runge-Kutta and fourth-order Gear predictor-corrector methods. These comparisons, were performed based on several transport properties of Lennard-Jones fluids: self-diffusion, shear viscosity and thermal conductivity. Because transport properties involve long time simulations to obtain accurate evaluations of their numerical values, they provide an excellent basis to study the accuracy and stability of the Sl methods. To our knowledge, previous studies on the SIs have only looked at the thermodynamic energy using a simple model fluid. This study presents realistic, but perhaps the simplest simulations possible to test the effect of the integrators on the three main transport properties. Our results suggest that if an algorithm fails to adequately conserve energy, it will also show significant uncertainties in transport property calculations.