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Lateral inhibition is an important functionality in neuromorphic computing, modeled after the biological neuron behavior that a firing neuron deactivates its neighbors belonging to the same layer and prevents them from firing. In most neuromorphic hardware platforms lateral inhibition is implemented by external circuitry, thereby decreasing the energy efficiency and increasing the area overhead of such systems. Recently, the domain wall -- magnetic tunnel junction (DW-MTJ) artificial neuron is demonstrated in modeling to be inherently inhibitory. Without peripheral circuitry, lateral inhibition in DW-MTJ neurons results from magnetostatic interaction between neighboring neuron cells. However, the lateral inhibition mechanism in DW-MTJ neurons has not been studied thoroughly, leading to weak inhibition only in very closely-spaced devices. This work approaches these problems by modeling current- and field- driven DW motion in a pair of adjacent DW-MTJ neurons. We maximize the magnitude of lateral inhibition by tuning the magnetic interaction between the neurons. The results are explained by current-driven DW velocity characteristics in response to external magnetic field and quantified by an analytical model. Finally, the dependence of lateral inhibition strength on device parameters is investigated. This provides a guideline for the optimization of lateral inhibition implementation in DW-MTJ neurons. With strong lateral inhibition achieved, a path towards competitive learning algorithms such as the winner-take-all are made possible on such neuromorphic devices., Comment: 8 pages, 5 figures