Catalyzes both the ATP-dependent activation of exogenously supplied lipoate to lipoyl-AMP and the transfer of the activated lipoyl onto the lipoyl domains of lipoate-dependent enzymes. In the mitochondrion, functions as a redox switch between two lipoylation routes. Senses the oxidation state of lipoate and determines which downstream enzymes will be lipoylated. In low reducing conditions, uses lipoate in its oxidized ring form to lipoylate glycine cleavage system H-protein GCVH. In high reducing conditions and together with LipL2, uses reduced lipoate (dihydrolipoate) to lipoylate the E2 component of the branched chain alpha-ketoacid dehydrogenase complex BCKDH-E2/BCDH and the E2 component of the alpha-ketoglutarate dehydrogenase complex KDH. LipL1 is responsible for catalysing the activation of lipoate, forming lipoyl-AMP while LipL2 is required but is not capable of catalyzing this reaction