My understanding is they only offer soy milk onboard, at least that is what all the people in the Vegan's Cruizin With Carnival FB group report form their trips.
You can call/email special access, but they will probably tell you they can only accommodate you in the main dining room. This is false. I recommend emailing the Maître D.
On embarkation day, go to the Maitre D's check in area and talk to them about the fact that she is lactose intolerant. They should help you figure it out. Then each night, you should be able to pre-order for the next night/day and know what does and does not have dairy in it.
In the lido deck, they have what is called "Menu Mate" stands which you can input what you can't have and it lists what's on the menu that she can eat.
Be careful on specialty restaurants- they don't always list everything. Like the pasta Cucina place- they don't say they add cheese on top, but they do.
Be ready to ask and talk to everyone before you eat and be prepared for it to take longer.