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.