Luna's intent to burn the body was simply to erase as many remaining clues as possible with her own methods.
As long as she could prevent any clues from leading back to her, that would be enough.
This was the promise she had made and indeed desired to fulfil: to destroy all traces and keep herself hidden from others.
However, at this moment, the man in front of her unexpectedly made this request.
This was a once in a lifetime opportunity to observe someone up close while they were completely oblivious.
It was much more real than observing someone's every move through Magic Projection.
Furthermore, Luna could also influence the other's actions with her own behaviour, thereby discerning what the other person really wanted to do.
She could then infer their character from their actions.
If Luna could understand someone's character and disposition, especially when that person was an enemy and completely unaware of her, her advantage would be significant.