Vegetarian Lacto-Ovo (VLML) will often contain cheese as it's pasta. Vegetarian Vegan (VGML) meals will not likely have cheese, but are pretty poor in taste and unappetising. That's a matter of my own opinion.

YMMV, if you want to be sure of no meat/cheese then order VGML and you'll be safe, but then no guarantees on whether you'll actually enjoy the meal.

On CX J the standard main course choices on USA flights may not necessarily always have a fish option, but for one meal there will be at least one vegetarian option, but this is usually a pasta and will likely have cheese.