Is it possible that by mutation a human could see infrared or other 'colours'?
Yes.

Far-red vision (>700nm)

The ability for retinal-binding proteins to absorb far-red (between 700nm-850nm) light has been experimentally confirmed in this paper. While the authors did not attempt this in vivo in an animal model, they managed to use directed mutagenesis to induce a significant shift in the absorption peak of the chromophore of the retinal binding protein. 

The authors show the shifts induced by these mutant proteins in the figure below. The mutants have significantly different absorption peaks, and assuming that the proteins do not lose their ability to transduce signals via optic nerves, they would allow vision in different wavelengths. 



Ultraviolet vision (300-400nm)

It is known that humans lacking a lens (aphakia) are able to see ultraviolet light. As noted in the question, the lens blocks out long-wave UV, and its removal or absence results in ultraviolet vision (although with low sharpness due to the lack of a lens). 


  However, aphakic patients report that the process has an unusual side effect: they can see ultraviolet light. It is not normally visible because the lens blocks it. Some artificial lenses are also transparent to UV with the same effect. The receptors in the eye for blue light can actually see ultraviolet better than blue. Military intelligence is said to have used this talent in the second world war, recruiting aphakic observers to watch the coastline for German U-boats signalling to agents on the shore with UV lamps.