Here's why:

* Autotrophs are organisms that make their own food through photosynthesis. They use sunlight, carbon dioxide, and water to produce sugars. Plants are the classic example of autotrophs.

* Heterotrophs are organisms that cannot make their own food. They obtain their energy and nutrients by consuming other organisms. This includes animals, fungi, and some bacteria.

Lilies, like all plants, are capable of photosynthesis and thus produce their own food. However, they are not autotrophic because they rely on external sources for nutrients like nitrogen, phosphorus, and potassium. These nutrients are absorbed from the soil through their roots.

So, while lilies can make their own food, they still need to obtain other essential nutrients from their environment, making them heterotrophic.