Connecting LED to a microcontroller powered with CR2032 with discharge voltage range 3.3V to 2V
If you don't mind a few more parts you could connect the LED to a voltage doubler, but you'd only get ~half the LED current for the same input current. 







simulate this circuit &ndash; Schematic created using CircuitLab

(not shown) use a large bypass cap across the battery- 100uF would be good. 

Or just find the LED with the lowest Vf you can find (it will be a red color).