The lens is in front of the sensor, so the sensor cannot get any more details than the lens lets through. That is why if your lens is of poor quality, your images appear blurry.

Now, it is never better to shoot at a lower resolution because the lens resolves a fixed amount of details in a given state (focal-length, aperture and focus-distance). At worst, you will have exactly the same amount of details, just sampled at a lower resolution. When viewed at 100%, it will look less blurry, yes, but you would not be comparing the same image size. Now, you can decide to save memory and bandwidth if you only need smaller images and that is OK.

The higher the resolution of your camera, the more demanding it is of lenses in order to take advantage of the full resolution. You will often see this comment DPReview's review conclusions.

Given that sharpness of a lens is very depending on all its settings and even spatially variant (corners are rarely as sharp so the center), I would not recommend lowering the resolution. In general, a lens gets sharper as the aperture is stopped down, up to its maximum sharpness and then sharpness gets reduced when the diffraction limit is hit. How much very much depends on the lens. High quality lenses for example may be only a tiny bit softer wide-open while low quality lenses can become extremely blurry. So, if your photos are too soft, you can try to stop down, usually 2 stops from the maximum is the rule of thumb.