Is a noisy laptop fan caused by dirt on the fan?

While it's possible that dirt in a fan could potentially cause noise, what's much more likely is that the bearing(s) in the fan are starting to fail or otherwise seize. This creates a grinding noise that can get progressively worse if not taken care of. Eventually the fan may stop spinning altogether, and then you'd have more to worry about than the fan.

It's also possible that the noise you're hearing is from the hard drive, but if it is noticeably loud it's most likely the fan.

If you're not comfortable opening the laptop up and inspecting/replacing parts, I would suggest taking it into the shop.

I'd say bad bearing - the sound going noisy and quiet is due to the fan shifting around somewhat. It can also be lower pitched depending. Youtube has quite a few examples such as this. The fan may last a while but at the end of the day, its a race between your patience, and the fan dying. Get it fixed.

Yes very true, but sometimes there could be another reason along with the dirt, first try to blow out the dirt/dust from the fan, and see if the noise is reduced, if there is no reduction in noise then you must consult a maintenance service.