LED Forward Voltage Higher Than Source
Nothing will break, nor will anything light up.

If you must use the LED, you need a secondary voltage source. One can be made using a step-up circuit or boost-converter, and there are likely many questions about that here.

Another option is taking a secondary voltage in, for example 5 volt from any USB charger and just use the Arduino to control it, using a transistor. This might work, though it's cutting it a bit close.