Would this parallel LED lamp upset the working of the flywheel diode?
No, you have nothing to worry about, assuming you have chosen the correct diode for your design.  The current from the solenoid will flow through the diode as normal, especially if your lamp is an LED.  The fly-back diode will clamp the reverse voltage to about 0.8V or so (its diode drop). Be sure your lamp can handle this reverse voltage.  Then there should be no concerns.  

If you lamp is just an LED in series with a resistor, the LED will be reverse biased and no current will flow in the lamp. If there's any active circuitry in it just be sure it can handle the ~ .8V of reverse voltage across it.