Things kind of break down for me when I think about what would happen if it were somehow possible to build a wing with infinite aspect ratio. Induced drag would be zero. But would that mean that drag was independent of lift?
No. To get greater lift at a given airspeed (for example because of a higher total weight), you'd need a higher angle of attack. A higher angle of attack means more parasitic drag. Because there's no induced drag, I guess you'd say that the higher drag was caused by the higher angle of attack, not the higher lift. But can you really separate the two?