This study investigates the decay mechanism of composite systems populated through complete fusion (CF) and incomplete fusion (ICF) channels of the reaction [6]Li + [90]Zr in the beam energy range 13-30 MeV using the Dynamical Cluster-decay Model (DCM). The low threshold energy and exotic structure of [6]Li makes it susceptible to break-up into smaller fragments ([6]Li→ [4]He + d) and significantly influences the fusion dynamics, which is a fascinating case study in low-energy heavy-ion reaction (HIR) physics. A suppression in the CF cross-section is expected at the subbarrier and above barrier energy regimes, owing to the significant probability of [6]Li fragmentation in the force field of target nucleus. The determination of Complete fusion (CF) and Incomplete fusion (ICF or breakup) cross-section is interesting for both experimental and theoretical nuclear physicists because fusion and exit-channel modes of weakly bound projectile are different from of strongly bound projectiles, necessitating precise measurements and sophisticated model calculations to disentangle the contributions from various reaction channels. In the present analysis, a novel methodology is employed to determine the Complete fusion and Incomplete fusion cross-section for the aforementioned reaction. The DCM model is employed to analyze the decay process by fixing the only parameter (neck-length; ∆R). Our results show good agreement with experimental data for all incident beam energies and provide new insights into the mechanisms governing the breakup of loosely bound projectiles. The implications of our findings for nuclear physics research are discussed.