Correct sentence: The lungs put oxygen into the blood.
Easy alternative: The lungs fill the blood with oxygen. (Adding "the" makes it sound better.)
Why this is correct: We say "the lungs" because we mean the lungs inside your body. "Put oxygen into the blood" is a simple way to explain what the lungs do.
Child-friendly example: When you breathe, the lungs take air and give oxygen to the blood so your body can use it.