Aging has been associated with the accumulation of damages in molecules and organelles in cells, particularly mitochondria. The rate of damage accumulation is closely tied to the turnover of the affected cellular components. Perturbing mitochondrial turnover has been shown to significantly affect the rate of deterioration of mitochondrial function with age and to alter lifespan of model organisms. In this study, we investigated the effects of upregulating autophagy using lithium in Caenorhabditis elegans. We found that lithium treatment increased both the lifespan and healthspan of C. elegans without any significant change in the mortality rate and oxidative damages to proteins. The increase in healthspan was accompanied by improved mitochondrial energetic function. In contrast, mitochondrial DNA copy number decreased faster with age under lithium. To better understand the interactions among mitochondrial turnover, damage, and function, we created a mathematical model that described the dynamics of functional and dysfunctional mitochondria population. The combined analysis of model and experimental observations showed how preferential (selective) autophagy of dysfunctional mitochondria could lead to better mitochondrial functionality with age, despite a lower population size. However, the results of model analysis suggest that the benefit of increasing autophagy for mitochondrial function is expected to diminish at higher levels of upregulation due to a shrinking mitochondrial population.