Lobsters have basically unlimited telomerase which acts as buffers for chromozones, preventing aging. Humans have a set limit of telomeres which applies to the Hayflick limit. That said, Lobsters will keep growing until they can't molt anymore and slowly succumb to disease or are crushed to death but when they stop molting is not necessarily known as they are usually killed/harvested before they can get too big.
Kid I went to school with's dad was a fisherman and had a massive claw from a lobster he caught in like the 70s or something. It was bigger than my hand. Granted I was only in 5th grade but it was still huge.