In general, lenses do not degrade in this way. However, some old lenses made up until the 1970s contain elements made of thorium oxide — a radioactive element which yellows as it ages. These were used because they have a different refractive index, with low dispersion — so, generally, better-quality lenses, just as fluorite crystal or other exotic elements are used today. It's also possible that adhesives (used to bond lens elements to each other) or coatings used in older lenses may yellow as they age. In both of these cases, if there's enough effect to make a difference, you should see it when just looking through the lens.

The other difference may be in newer lens designs vs. older ones. This shouldn't affect the case your friend is talking about (same model over time), but may be the source of the confusion. Design of coatings changes, as does the types of glass used. And this can be very strong between manufacturers — for example, while I haven't found this anywhere official, many people believe Sigma intentionally introduces a slight color warming effect in their lenses.