Here's why:
* Direct Object: The direct object is the thing being acted upon by the verb. In this sentence, the direct object is "a lecture". Adriel is giving *something*, and that something is a lecture.
* Indirect Object: The indirect object is the person or thing that receives the direct object. The sentence doesn't specify who or what is receiving the lecture. We know it's *for* Adriel's brother, but he isn't directly getting the lecture itself.
To include an indirect object, you could rephrase the sentence:
* Adriel is giving *her brother* a lecture. Now, "her brother" is the indirect object, as he's the one receiving the lecture.
Let me know if you'd like to explore other ways to change the sentence!