LED in parallel with MOSFET
If the mosfet gate voltage is low, the leakage current will go into the uA-nA range (or maybe even lower!). This means when the mosfet is off, it's like a resistor with a value well above 1MΩ. Then check the current through the LTV847 to make sure there is enough current to turn on the LED. You can check this in the datasheet here. Right now the LTV847 has rougly 10k of resistance in series with it. That means if the LED has a 2V drop only 2.2mA would be going through the LED.