The development of energy-efficient neuromorphic hardware using spintronic devices based on antiferromagnetic (AFM) skyrmion motion on nanotracks has gained considerable interest. Owing to their properties such as robustness against external magnetic fields, negligible stray fields, and zero net topological charge, AFM skyrmions follow straight trajectories that prevent their annihilation at nanoscale racetrack edges. This makes the AFM skyrmions a more favorable candidate than the ferromagnetic (FM) skyrmions for future spintronic applications. This work proposes an AFM skyrmion-based neuron device exhibiting the leaky-integrate-fire (LIF) functionality by exploiting either a thermal gradient or a perpendicular magnetic anisotropy (PMA) gradient in the nanotrack for leaky behavior by moving the skyrmion in the hotter region or the region with lower PMA, respectively, to minimize the system energy. Furthermore, it is shown that the AFM skyrmion couples efficiently to the soft FM layer of a magnetic tunnel junction, enabling efficient read-out of the skyrmion. The maximum change of 9.2% in tunnel magnetoresistance is estimated while detecting the AFM skyrmion. Moreover, the proposed neuron device has an energy dissipation of 4.32 fJ per LIF operation, thus paving the way for developing energy-efficient devices in AFM spintronics for neuromorphic computing.