What does an aperture do? It "applies" Huygens principle to every point within the aperture, and ignores those outside the aperture because they are blocked.
There are a couple of things going on when you consider a lens. Let's make sure we understand them.
An aperture produces a diffraction pattern in the space of diffraction angles. Recall from the simple derivation: the diffracted rays from every point in the aperture are parallel to each other. (The diagrams accompanying the discussion often have to be fudged so that parallel lines appear to converge, although some authors are careful to include a lens as described below.) The diffracted intensity is a function of diffraction angle. The diffracted field from the screen comprises sets of parallel rays, each set corresponding to a particular interference condition (max, min, or in between). Again, the diffraction pattern is in "angle space". In order to see the pattern you need to be far enough away from the aperture that the rays from different angles and different points in the aperture no longer cross each other causing a confused pattern. You need your viewing screen to be "at infinity".
Now consider what a lens does. Any set of parallel rays entering a lens will be focused to a single point in the focal plane.
Consider placing a lens after an opaque aperture. Any parallel rays entering the lens will be focused to a single spot in the focal plane. Hence all the rays in each set of parallel rays from the aperture will focus onto the same spot in the focal plane. We've created the usual "Fraunhofer pattern at the focal plane". Allow the aperture and lens to approach each other, and you end up with an aperture containing a lens, producing the usual Fraunhofer pattern on the focal plane.
To finally answer your question: remove the aperture and leave the lens. The rays that hit the lens behave as before, forming the diffraction pattern at the focal plane. The rays that fall outside of the lens are also diffracted, according to Huygens principle. But these do not pass through a lens. So the diffraction pattern from these rays stays in "angle space". They exist, and in fact some of those rays overlap the rays from the lens. But we don't see them because they are spread out and weak, and if you are close to the lens their rays cross in a confused manner. Note, however, that those rays outside of the lens do form a legitimate diffraction pattern, which could be viewed "at infinity". The pattern would be a dark spot surrounded by light, the complement of the pattern for an aperture. Look up Babinet's Principle for more details.