Some scientists argue that lobsters can live forever unless devoured, injured, or get sick. This is theoretically possible because all of its cells are capable of producing a regeneration enzyme called telomerase. As a result, its cells, allegedly, never get old granting him eternal life.
Mind you, humans have telomerase enzymes as well, but only in a few cells and only till we get old.
Whether immortal or not, there is no doubt that lobsters continue to grow their entire life and that they grow old very slowly. Moreover, like wine, they get better with age. For example, as lobsters mature they become more fertile.
Bonus fact: Lobsters are capable of regenerating whole limbs, even in old age.