Can you identify this LED?
Yes. It seems to be a 5mm bright white straw hat possibly with a nominal forward voltage of 3.2 volts at a nominal forward current of 20 mA.

What I mean to say this is a bog standard led and you could replace it with any typically 20mA at 3.2V led of various colors as long as it fits. Nothing special about it.

Also the reviews on that lamp are garbage. The lamps routinely fail, with dead leds. Likely a bad design in the regulation or over-driving the leds. Replacing the leds will only prolong the inevitable. At 20 bucks, your better off buying a better lamp.