We obtain an explicit characterization of the \( K \)-functional of a pair of weighted classical Lorentz spaces of type \( S \). We develop a method for obtaining such characterization based on a relation between the desired quantity and the \( K \)-functional of a specific couple of spaces of type \( \Lambda \), which are substantially more manageable than their companions of type \( S \). The core of our techniques is a subtle manipulation with respective fundamental functions. We present several applications, in particular we nail down a formula for the \( K \)-functional of a Lebesgue space and a classical Lorentz space of type \( S \) with a power weight, and using this formula we establish an inequality of a reverse Marchaud type.