Many lycanthropes take the form of short lived creatures such as rats. Lycanthropes fully become the animal they change into during the full moon, that is to say all statistics not solely physical statistics. Given that humans can live more than eighty years and rats live only two years; would a Wererats, spending significant time as a rat age much faster than a normal human?
I'm aware that a question was asked about the ageing of shapeshifted creatures, but that question handled the case where personality is retained. A dragon in human form or a druid in wildshape is wearing the form, and retains their mental statistics and personality. Lycanthropes shapeshifting is called out as special in the Monster Manual, so this may be a case of specific beats out general?
A D&D 5e answer is best, but previous editions are acceptable as well.