How do I make a transistor turn on at a certain voltage?
With bipolar transistors it's the current that controls the transistor, not voltage (though there is a minimal voltage). So, increasing the base resistor (R2) will make the transistor turn on at higher voltage than 1.5V).

If you want the LED to turn on when the voltage is below 1.5V *that is, invert what it is now) then you can do it like this:



Now when the transistor turns on, it shorts out the LED so the LED goes dark. When the base current drops below a certain level, the transistor will turn off and the LED will turn on.

You may have to find a suitable value for R1 so that the LED turns off completely when you want it to turn off. The power supply voltage (5V in my circuit) does not really matter, as long as R2 is suitable for the LED.