The mechanisms of mitochondrial dysfunction in Alzheimer's disease are incompletely understood. Using two-photon fluorescence lifetime microscopy of the coenzymes, NADH and NADPH, and tracking brain oxygen metabolism with multi-parametric photoacoustic microscopy, we show that activation of lysosomal mechanistic target of rapamycin complex 1 (mTORC1) by insulin or amino acids stimulates mitochondrial activity and regulates mitochondrial DNA synthesis in neurons. Amyloid-β oligomers, which are precursors of amyloid plaques in Alzheimer's disease brain and stimulate mTORC1 protein kinase activity at the plasma membrane but not at lysosomes, block this Nutrient-induced Mitochondrial Activity (NiMA) by a mechanism dependent on tau, which forms neurofibrillary tangles in Alzheimer's disease brain. NiMA was also disrupted in fibroblasts derived from two patients with tuberous sclerosis complex, a genetic disorder that causes dysregulation of lysosomal mTORC1. Thus, lysosomal mTORC1 couples nutrient availability to mitochondrial activity and links mitochondrial dysfunction to Alzheimer's disease by a mechanism dependent on the soluble building blocks of the poorly soluble plaques and tangles.