After installing the RC electronics the only thing I had left to do was to fix the lights. I re-used the LEDs that came with the car. Then I used 100 ohm resistors for the LEDs. The front lights are individual and each have their own resistor. The tail lights are coupled in series and only have one resistor. This should give the front lights more intensity than the rear lights.
I didn't do anything smart with the lights. They just go on when the car is turned on. I use the battery connector on the receiver to power the lights. This means that I have a stable 5V power supply so the light intensity won't be affected by the current draw by the motor under acceleration.
Some pictures of the car after assembly: