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According to Duden, aus voller Lunge schreien = sehr laut schreien Dict.cc provides the following translation: at the top of one's lungs = aus voller Lunge So, the sentence enquired about can probably be translated as Sie schrie aus voller Lunge.
Pons suggests: Sie schrie sich die Lunge aus dem Leib. This is also a common idiom and I don't think you get closer to the original.
You seem to be needing some anatomy details: How about Sie schrie aus vollem Hals Not quite the lungs, but close. And a common idiom in German.
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