Agile methods are all about delivering maximum business value, and minimum risk. Lean manufacturing is about reducing cycle time (takt), and waste (muda). Its focus is on customer pull. From this idea flow concepts like just-in-time delivery, and inventory reduction. The ultimate lean system being one where a customer order arrives at the point of sale, and the instructions flow all the way back to the point of obtaining the raw materials. The necessary tasks to create the desired item take place, flowing back down the chain to the customer, who receives their product. No batching, no storage, just value creation.
Lean manufacturing principles applied to the software delivery process lead inexorably to something that looks very much like the ideal agile team: Customer requests feature, team implements feature, one-click automated build-test-deploy cycle takes place, feature is live.
You might argue that such an idealised vision is oversimplification to the point of absurdity, but it provides an excellent target (agilists might say ‘test’), against which to measure process improvement efforts and assess current state. Very pleasing.