BUT you don't have to. You CAN re-express whole systems as partial systems with external forces. A ball falling to earth has a time-independent Lagrangian beca

BUT you don't have to. You CAN re-express whole systems as partial systems with external forces. A ball falling to earth has a time-independent Lagrangian because you neglect the earth's acceleration. The electron orbiting the hydrogen nucleus moves in a fixed potential for the same reason. "Draw the boundaries correctly" and you can't do physics.