You can use a fairly simple transistor circuit to invert the signal from the LED. When the LED voltage goes low, your transistor output would go high, and vice-versa.
You take your LED driver voltage, run that through a base resistor to limit the current going into the base of the transistor, ground the emitter, and have a resistor connecting the transistor’s collector to your +4 supply. The output comes off of the transistor’s collector.
When the LED is on, current flows through the transistor (base to emitter) turning it on. This makes the transistor conduct electricity, effectively shorting out the voltage divider created by the transistor and the resistor from collector to your +4 supply. When the LED turns off, the current stops flowing into the base of the transistor, the transistor turns off, and has a much higher impedance than the resistor on the collector, so the collector resistor pulls the output high.
The resistor values are not critical. You want the base resistor low enough that current from the LED driver will drive the transistor completely into saturation, but not so low that the base current will damage the transistor. On the output side, you want the collector resistor to be large enough that when the transistor switches on, the output voltage will drop close to zero, but low enough that when the transistor switches off that the output voltage floats up close to the supply voltage.
The output voltage will never go all the way to zero or to +4.
If you want something more complicated, a 555 timer circuit or maybe a small and cheap microcontroller will be a better solution. Microcontrollers are dirt cheap for some of the smaller ones, require little external circuitry, and can be programmed to do all sorts of complicated responses to inputs. The down side is that you need to be able to program them.