Would a transistor be the correct device?
You can use a comparator to pull this off in the most flexible way. One method is to connect a known voltage reference (say from a precision Zener reference) to the minus input of the comparator, and then a voltage-divided version of VM1 to the positive input. You would select the divider values such that VM1 * divider ratio allows a voltage of 4.3V at VM1 to become a voltage of reference + a few mV. When that condition is true, the comparator will output a '1' that can be used to directly drive the gate of a transistor or some other transistor / relay circuit.

If your 5V rail is fairly stable, you could use that as your reference input by dividing it down via divider and feeding it to the minus input as well, saving the external reference.

The comparator can likely be powered off your existing 5V rail as well. Common models include the LM311. You may see a difference between open-drain and push-pull models; the open-drain types will only ever pull down actively; otherwise the output value floats to whatever you pull it too. A push-pull will actively drive high and low.

Finally, you can leave a resistor option between the output and - input to allow you to tune hysteresis in the future.

Option two (to avoid the comparator) is to use a precision analog MOSFET (from ALD, for example) with a very tight threshold voltage. Fed with a divider,  this can then trigger other devices to turn on the lamp.