Abstract: The influence of the Lennard-Jones (LJ) potential on the adhesive contact between a hard-coated elastoplastic sphere and a rigid flat, as well as its impact on the static friction behavior at the micrometer scale, particularly at the level of roughness peaks, is comprehensively investigated using the finite element method. In this study, a detailed examination is conducted wherein the contact boundary between the hard-coated elastoplastic sphere and the rigid flat is meticulously assumed to be fully adhesive, adhering to a fully stick boundary condition. The initiation of sliding at the interface is determined by the criterion of vanishing tangential stiffness at the contact boundary, a critical factor that signifies the onset of plate sliding. The intermolecular forces between the rigid flat plate and the hard-coated elastoplastic sphere, derived from the Lennard-Jones potential, are calculated with precision using a modified Derjaguin-Muller-Toporov (DMT) adhesion model. This model is rigorously simulated and implemented within the Abaqus environment through the user subroutine, taking into account real-time variations in the separation distance between the elastoplastic sphere and the rigid plate during both normal loading and tangential displacement phases. This approach ensures the accuracy and fidelity of the simulation, capturing the nuanced interactions at the interface. The validity and reliability of the proposed adhesion model are thoroughly established by systematically comparing the simulation outcomes with existing experimental data and models reported in the literature. The results of this investigation revealed that at the microscale, specifically at the scale of surface roughness peaks, neglecting the contribution of adhesion can lead to substantial errors in predicting the maximum static friction coefficient. This is especially pronounced under conditions of low external normal loads, where the adhesive forces played a more dominant role. The study further demonstrates that the maximum static friction coefficient initially exhibited a linear increase with the augmentation of the hard coat thickness, eventually reaching an optimal peak value at a specific thickness, denoted by the dimensionless ratio t/R = (t/R)_m. Beyond this critical thickness, the maximum static friction coefficient was observed to decrease following a hyperbolic cotangent function with further increases in coating thickness, eventually stabilizing at a certain value. Additionally, the analysis highlighted that an increase in adhesive energy δ resulted in a corresponding increase in the maximum static friction coefficient μ, although the overall trend in its variation with coating thickness remained unchanged. The adhesive energy δ was shown to have a negligible impact on the critical thickness (t/R)_m when the material parameters remained constant. Finally, the study delved into the effects of dimensionless material parameters, revealing that with an increase in the dimensionless parameter E_co/E_su, the influence of adhesive energy δ on the maximum static friction coefficient μ diminishes. In contrast, for a constant dimensionless load P^*, an increase in E_co/Y_co was found to enhance the proportion of adhesive force relative to the total external normal load, thereby amplifying the effect of adhesion energy on the static friction behavior. This comprehensive investigation provided valuable insights into the complex interplay between coating thickness, adhesive forces, and material parameters in determining the static friction characteristics at the microscale.