She does, and it is! However, it decides not to claim her!

Ikaros, after a moment of examining the lamp, started to idly brush it with her hand, and smiled softly at the smooth feel. It was actually quite warm... then, a burst of glittering pink mist erupted out, and engulfed her face. She blinked, but showed no further reaction, detecting no hostile intent, or anything potentially harmful to a human, much less an Angeloid in the vapors.

The smoke seemed to hold the essence of some sort of entity, one that Ikaros got the strangest feel was... assessing her in some way. Then, it started to communicate with her. Not with words though, but with... concepts was the only way to describe it.

The Lamp "explained" to her that it was seeking a vessel for its power, to become an eager genie **** to whoever possessed it. It had strongly considered her, but seeing she was already a subservient, powerful entity, it almost considered making her into the sex genie a waste. It could also tell that she would want to give it to Tomoki, ensuring he had it.

Therefore, it was proposing instead to task her with finding someone else to put inside it, and then the Lamp could be given to Tomoki by her. He could have two powerful servants instead of one then. Ikaros, able to sense what being a genie would be like, almost insisted on being claimed herself... but the Lamp had a point, it would barely enhance her nature. And it definitely appealed to her to ensure Tomoki had someone else to serve him alongside her. Plus, the risk of someone else finding the Lamp also didn't appeal. So she nodded assent, and the mist retreated back into the Lamp.

Holding it in her hands, she considered who best to find for Tomoki. After a moment of consideration, she said to herself, "Sohara Mitsuki." Yes, Tomoki's childhood friend would be perfect for this. Noticing the Lamp had dressed her in a school uniform while the mist had been out after she accepted its proposal, no doubt to keep her incognito, she shrunk down her wings and headed into the building.