A Lefschetz fibration structure on manifold is a map from the manifold to a complex curve whose fibers are Riemann surfaces, some of them are singular. Lefschetz fibrations is applicable to questions about cloed symplectic 4-manifolds, in light of a theorem of Gompf that a Lefschetz fibration on a 4-manifold X whose fibers are nonzero in homology gives a symplectic structure on $X$ and a theorem of Donaldson that, after blowing up a finite number of points, every symplectic 4-manifold admits a Lefschetz fibration structure. A Stein manifold is a complex manifold which admits a proper complex embedding into $mathbb{C}^N$. By intersecting with a large ball in $mathbb{C}^N$, we obtain a compact symplectic manifold with contact boundary called a Stein domain. As in the closed case, a $4$-manifold $X$ admits a Lefschetz fibrations with bounded fibers if and only if it is a Stein domain. We investigate the isomorphism classes of Lefschetz fibration structure on knot surgery $4$-manifolds using the representation of the monodromy group . Also we provide an algorithm for Lefschetz fibration structure on the Stein fillings of links of quotient surface singularities and show that they are related by rational blow downs.