The paradox arises because cost per unit fuel does not decrease because of use-efficiency. Whether your car gets 20 miles to the gallon or 50, you pay the same price per gallon at the pump.
Therefore, in an "all other things being equal" sense, you'd expect more efficient use of the fuel to lower total consumption, since the same desired effect is achievable with less input. Switching from incandescent lights to LED lighting should lower your electricity bill.
The paradox arises because of an income effect or "standard of living" effect, as you note, and it arises as "all other things being equal" gives way to a new equilibrium. It's not guaranteed to happen -- I imagine few people's electricity bills have gone up because they use so much more LED lighting than incandescent lighting -- but it can happen.
Therefore, in an "all other things being equal" sense, you'd expect more efficient use of the fuel to lower total consumption, since the same desired effect is achievable with less input. Switching from incandescent lights to LED lighting should lower your electricity bill.
The paradox arises because of an income effect or "standard of living" effect, as you note, and it arises as "all other things being equal" gives way to a new equilibrium. It's not guaranteed to happen -- I imagine few people's electricity bills have gone up because they use so much more LED lighting than incandescent lighting -- but it can happen.