You should read the wiki for biological immortality:
Biological immortality (sometimes referred to as bio-indefinite mortality) is a state in which the rate of mortality from senescence is stable or decreasing, thus decoupling it from chronological age. Various unicellular and multicellular species, including some vertebrates, achieve this state either throughout their existence or after living long enough. A biologically immortal living being can still die from means other than senescence, such as through injury, disease, or lack of available resources.
Interestingly, the article cites lobsters:
Research suggests that lobsters may not slow down, weaken, or lose fertility with age, and that older lobsters may be more fertile than younger lobsters. This does not however make them immortal in the traditional sense, as they are significantly more likely to die at a shell moult the older they get (as detailed below).
Their longevity may be due to telomerase, an enzyme that repairs long repetitive sections of DNA sequences at the ends of chromosomes, referred to as telomeres. Telomerase is expressed by most vertebrates during embryonic stages but is generally absent from adult stages of life. However, unlike vertebrates, lobsters express telomerase as adults through most tissue, which has been suggested to be related to their longevity. Contrary to popular belief, lobsters are not immortal. Lobsters grow by moulting which requires a lot of energy, and the larger the shell the more energy is required. Eventually, the lobster will die from exhaustion during a moult. Older lobsters are also known to stop moulting, which means that the shell will eventually become damaged, infected, or fall apart and they die. The European lobster has an average life span of 31 years for males and 54 years for females.
So all you need to do is find a way for your titanic lobster to either repair its shell or survive its moulting as it grows bigger - neither is too large a stretch. It could happen realistically. In our own world lobsters evolving to be gigantic might be improbable, but not impossible.
I just remembered that the ancerstors of crustaceans could grow up to 2m long. That they never grew bigger is a matter of evolutionary pressure, which could have happened differently in your world.