I recently watched the XL season I-Spy episode from 2011 where the age of lobsters were discussed.
I just wanted to add a note that this is now possible to determine by studying the growth bands in the gastric mill ossicles (looks the same as tree rings and fish otoliths).
Kilada et al, 2012. Direct determination of age in shrimps, crabs,
and lobsters. Can. J. Fish. Aquat. Sci. 69: 1728–1733.
Kilada et al, 2015. Feasibility of using growth band counts in age determination of four crustacean species in the northern Atlantic. Journal of crustacean biology 35(4): 499-503.