They can actually eat your plants. I'm not saying it happens all the time per say, but if there is a lack of food they and their larvae CAN eat your plant. I don't think they can eat a whole plant or anything, but...
I have never seen a lady bug eat a plant. I have seen large holes in leaves caused from an aphid or mildew infestation where there were also lady bugs present, but have never witnessed lady bug larvae eating plant matter.
From ohio University Fact sheet:
Lady Beetle, HYG-2002-98
"Lady beetles, both adults and larvae, are known primarily as predators of aphids (plant lice), but they prey also on many other pests such as soft-scale insects, mealybugs, spider mites and eggs of the Colorado Potato Beetle and European Corn Borer. A few feed on plant and pollen mildews. One larva will eat about 400 medium-size aphids during its development to the pupal stage. An adult will eat about 300 medium-size aphids before it lays eggs. About three to ten aphids are eaten for each egg the beetle lays. More than 5,000 aphids may be eaten by a single adult in its lifetime. The lady beetle's huge appetite and reproductive capacity often allow it to rapidly clean out its prey.