This article develops two algorithms for the thermal Lattice Boltzmann Method (LBM) to simulate supercritical fluid dynamics using real-fluid thermodynamics. The first algorithm employs a compressible formulation (LBM-C), while the second is based on a Low Mach Number approximation (LBM-LMN) to enhance computational efficiency without compromising physical fidelity. Both approaches use a conservative scheme compatible with cubic equations of state (EOS), enabling accurate representation of non-ideal behaviors under supercritical conditions and ensuring mass, momentum, and energy conservation. Validation on canonical supercritical flow benchmarks demonstrates that the LBM-LMN approach achieves accuracy comparable to the compressible formulation while reducing the overall computational time by a factor of about 15, as quantified by the RTTS parameter.