If you read for instance the
Digital Cameras, Digital Camera Reviews - The Imaging Resource! camera reviews, you will see how other cameras handle image noise.
Don't be fooled by apparent low noise on first sight, many camera's have noise reduction algorithms inside, removing noise at the cost of image detail.
Many photographers believe that they should be in control over noise reduction in post processing, so I advise you to study the RAW image examples best.
In general terms lenses do not add noise to an image.
However, lenses with a lower f number will be able to deliver more light to the sensor, making it possible to avoid higher ISO settings with the same light (at the cost of "depth of field").
Remember when you increase your ISO number, you will be amplifying the sensor signal more, before it is digitized. It is like turning up the volume. Any noise in the signal will be amplified with the image signal itself. Like with sound noise is more noticeable with low signals (dark parts of the image).
- Bert