This research article investigates two subclasses of bi-univalent functions associated with (s, t)-Lucas polynomials in 𝔻. It intriguing since they are fundamental to geometric function theory. To understand the geometrical properties of these subclasses, the estimates of two initial Taylor-Maclaurin coefficients |a2| as well as |a3| are very essential. These play a vital role to explore a number of significant geometric features of subclasses. These initial coefficients provide significant information about the behavior of the function near the origin, revealing its functional characteristics, interaction with the boundary of the unit disk, and possible subclassifications. In particular, their distortion, growth behaviour, and mapping qualities. Additionally, we employ the Fekete-Szegö approximation, a technique frequently employed to derive precise constraints for these two subclasses, which traditionally gives upper bounds for |a3 – τa22|.