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So you want the lights to go off when you close the switch?
If so, you could use the circuit in Figure 2 of your reference with a slight modification. Change R1 to about 5kΩ (for 20mA LED current) and connect its input to the plus voltage. (You can remove R2, it's not needed for this circuit.) This will turn the transistor and LEDs on with no input.
Also connect the transistor base input to the NO switch with the other switch end connected to ground. Then when you close the switch it will remove the transistor base drive and the transistor will turn off.
Make sure you have the proper sized resistor in series with LEDs to give the desired LED current.