A N-Channel MOSFET is switched ON by a positive charge on its gate relative to its source. As long as the gate-source voltage is higher than Vth, the MOSFET is "on". (Of course there are partially-conducting ranges but I assume your intention is to saturate it, i.e. switch on "hard".)
In your circuit, it is unclear what the source voltage will be relative to the gate when the lower circuit is not pulling the source to ground, mostly because it is an "unknown design". Furthermore, I am not sure what you are trying to accomplish with your N-Channel MOSFETs. When they are switched on, all of the lamp current still flows into your lower circuit. In other words, they are not enhancing the driving current of the lower circuit in any way; you could just connect your lamps directly to the lower circuit and dispense with the MOSFETs.
I would consider two different approaches:
Use P-Channel MOSFETs in the upper circuit, and switch the positive side of the lamps. The gates can be driven by the lower circuit. Choose MOSFETs with a wide enough gate voltage range (e.g. > ±15V) and protect the gates with a series resistor and a zener from gate to source.
Use a voltage divider and logic inverter on the output of the lower circuit, and drive your N-Channel MOSFETs with that inverted signal. Keep the MOSFET source terminals permanently tied to ground.
Combine your microcontroller's outputs with the lower circuit's state using NOR gates:
R1 and R2 form a voltage divider suitable for converting 12V vehicle signals to 5V logic signals. D1 is to protect the logic inputs from possible voltage spikes.
The voltage divider presents less than 1 mA of load, but you may find it weakly "turning on" the vehicle's original lighting. Be sure to take a look in the dark, and measure current into this input with a multimeter with all lights and vehicle off, to be sure it doesn't put a small but ongoing drain on the vehicle's battery. If any of this turns out to be the case, there are other ways of buffering the input to prevent it.