The time-scales associated with various stages of the star formation process represent major unknowns in our understanding of galactic evolution, as well as of star and planet formation. This is the second paper in a series aiming to establish a multi-tracer time-line of star formation in the Large Magellanic Cloud (LMC), focusing on the lifecycle of molecular clouds. We use a statistical method to determine a molecular cloud lifetime in the LMC of $t_{\text{CO}}=11.8^{+2.7}_{-2.2}$ Myr. This short time-scale is similar to the cloud dynamical time, and suggests that molecular clouds in the LMC are largely decoupled from the effects of galactic dynamics and have lifetimes set by internal processes. This provides a clear contrast to atomic clouds in the LMC, of which the lifetimes are correlated with galactic dynamical time-scales. We additionally derive the time-scale for which molecular clouds and H ii regions co-exist as $t_{\text{fb}}=1.2^{+0.3}_{-0.2}$ Myr, implying an average feedback front expansion velocity of 12 km s−1, consistent with expansion velocities of H ii regions in the LMC observed directly using optical spectroscopy. Taken together, these results imply that the molecular cloud lifecycle in the LMC proceeds rapidly and is regulated by internal dynamics and stellar feedback. We conclude by discussing our measurements in the context of previous work in the literature, which reported considerably longer lifetimes for molecular clouds in the LMC, and find that these previous findings resulted from a subjective choice in timeline calibration that is avoided by our statistical methodology.