A lens focuses light because there is refraction at the air/glass and glass/glass surfaces. Refraction is not a bad thing in a lens, it is a good thing - essential in fact. The lenses we commonly use work because of refraction.
Destructive interference ('gaps') caused by diffraction is rarely a problem in normal photography because the light arriving at the aperture is not usually coherent - ie the 'overlaps' of light heading to two different image points caused by diffraction rarely cause destructive interference because the overlapping light in this case is not usually at the same frequency and in a constant phase relationship. The effect is generally to spread light that should have focused to a single point into a spread-out interference pattern with a central disk (the Airy disk) surrounded by rings (all of which is the Airy pattern). The loss of (otherwise possible) detail happens not because of gaps but because image points are spread into disks. Of course there are other factors in a real lens that will also cause a point to spread (such as lens aberrations, defocus etc) so diffraction simply sets a minimum possible amount of spread.