Why does my desk lamp(LED) seems to flicker very fast when capturing through camera lens?
There can be several reasons for LED lights to flicker. Most were mentioned in comments above. I’ll summarize them in one answer. (Note that the one actual answer, “All LEDS flicker” is wrong.)
LED brightness is controlled by the amount of current that feeds them. Usually that is controlled with supply voltage.
A cheap power supply can have voltage fluctuations, which will cause the brightness to flicker.
A REALLY cheap power supply might use half-wave rectification, which clips off the negative half-wave of the AC supply, causing the LED to flash on and off with the positive half of the AC sine wave (60 Hz in the US, 50 Hz in much of the rest of the world.) It’s also possible the power supply is low voltage AC, and the LED just blocks the negative half of each cycle. The effect of either of these would be for the LED to be on half the time and off half the time, probably at the frequency of your AC power.
Some LEDs lights control their brightness using pulse-width modulation (PWM). This varies the percentage of on time to off time to change the average brightness. Usually this is done quite fast, and and our eyes perceive the average brightness. If the PWM frequency is high enough (10s or 100s of kHz) it takes a very fast camera shutter-speed for it to show up at all.
Other LED setups like calculator LED displays and other grids of LEDs multiplex a large number of LEDs by lighting them in groups and cycling between those groups rapidly. At any instant only a fraction of the LEDs that appear lit actually are lit.