It's like too late to talk to the special needs dept., but they may want to try that.
But, even without, there's always vegetarian choices available. The problem might arise if they are vegans. But if they were, one would think they would have checked out the availablity of food to match their diets before now.
Although I put in my profile vegetarian I doubt they did anything special for me. I was on the Celebrity in 2004 and they had a wonderful vegetarian selection. They had a separate menu in the dining room for vegetarians. Some of the items may have been the same things as on the regular menu some were different. My waiter also would show me the menu for the next night before leaving the table. One day I noticed they were having black bean soup for lunch which I love but we never came to the dining room for lunch. He saved it for me for dinner. Also, the had and Indian Chef who cooked their Italian food. He made special Indian vegitarian meals for me. Now that is not always going to happen I just lucked out. Your parents are probably fine. If their waiter has no clue what the vegetarian menu then just ask the assistant matra d' who they will meet that first night. And I'm sure they can make arrangements to see the menu for the next day as well before they leave. I'm going to try and do that for my December cruise for both the Vegi menu and the Children's menu so that if I need to make any special arrangments I can.