Exclusive measurements of prompt γ-rays from the heavy-residues with various light charged particles in the ⁷Li+¹⁹⁸Pt system, at an energy near the Coulomb barrier (E/V_b ~ 1.6) are reported. Recent dynamic classical trajectory calculations, constrained by the measured fusion, α- and t-capture cross-sections have been used to explain the excitation energy dependence of the residue cross-sections. These calculations distinctly illustrate a two-step process, breakup followed by fusion, in case of the capture of t and α clusters; whereas for ⁶He+ p and ⁵He+d configurations, massive transfer is inferred to be the dominant mechanism. The present work clearly demonstrates the role played by the cluster structures of ⁷Li in understanding the reaction dynamics at energies around the Coulomb barrier