I have been eating gluten free for about 12 years now and have sailed with Royal Caribbean, Celebrity, and Disney.
Celebrity Mercury did the best job of ensuring I did not have any problems. I was convinced the MDR staff were psychic as everyone seemed to know I needed gluten free and I never had to say anything twice. Only complaint was that the gf bread was bland and dry, but nobody ever tried to serve me regular bread. Celebrity got an A+
RCCL Mariner of the Seas did a pretty good job in the MDR and room service. I did feel the need to remind my servers occasionally--after eating gf for this many years, I can tell who "gets it" and who doesn't. But in the end they came through and I had no problems...until I went to the specialty restaurant, I'm pretty sure it was Chops. During dinner I started to feel bad (I'm very sensitive and have an almost immediate neurological reaction) the waiter swore everything he brought us was GF but a little later he came back to the table and said the Chimichurri sauce was not. Since I had to be more diligent and alert, RCCL got a B
Disney Wonder chefs were fine, but the waitstaff was surprisingly clueless. My second night I ordered onions on my steak. The waiter was arguing with me that I could not have onions because onions aren't GF.
He couldn't explain why, but he knew it was so. Turns out, I couldn't have THESE onions because they were breaded and fried! I found this out because he brought them to me "on the side"...but on the side of my plate, touching my other food, not on a separate plate.
On all three lines, this is how the routine went:
Notify the cruise line well before your trip. Then, be sure to go to the dining room on embarkation day and discuss your dietary need with the Maitre d'. He might show you a menu and have you "pre order" your meal, or he might tell you the items you can have that night. Then each night toward the end of your dinner, he or the head waiter will take your order for the next night so they can plan and prepare accordingly.
I never eat at the Lido...people will unknowingly cross contaminate going from one dish to another with a utensil, plus the servers are usually way too busy to stop what they are doing to go back to the kitchen to ask the chef about ingredients, etc.
In general, cruising is one of the safest vacation options for us GF folks.
The cruise industry is really pretty dialed in on the topic.
I hope you have a great, healthy, gluten free trip!