Noise is a sensor / ISO issue.
Actually all pictures have noise. This brings us to the concept of “signal to noise ratio.” If the signal (image quality) is really strong, say broad daylight at 100 ISO, the signal ratio is very high and the noise ratio is so low you probably can’t detect it. It’s minute. So your picture is, say, 99 percent signal and 1 percent noise. Nice looking picture.
In low light situations when the ISO is high, the camera (or sensor) has trouble seeing. That's why your auto focus doesn't work so well in low light. The image signal is not strong enough to keep the noise ratio down so the camera fills in the blanks with noise. It’s the camera’s way of saying, “I really can’t see that well.” The signal to noise ration could be, say, 60 / 40. 60 percent picture and 40 percent “I can’t see that well” noise.
Heat also creates noise. Not hot outside but a hot sensor. If your shutter is open for long periods of time (as it is in low light) and your sensor is collecting data, it gets hot, thus helping create noise. Some sensors (and firmware) handle noise better than others.
I’m sure someone will come along and explain this even more simply than me. But no, noise does not come from your lens. However, really slow lenses can contribute because you must use slower shutter speeds in low light to get the image.