English Translation
Lack of food made them very hungry.
Unnatural word-for-word translation. We don’t use “lack of food” (食糧不足) as a subject in Japanese. It should be:
食料不足で彼らは腹ペコだった。（しょくりょうぶそくでかれらははらペコだった。）= (lit.) They were very hungry due to lack of food.
彼らが腹ペコなのは食料不足のせいだ。
Both 食料 and 食糧 are pronounced as しょくりょう, but 食料 is better in this context. For more details, please refer to this article.
食糧 is limited to rice or wheat, and it excludes meat and other vegetables/fruits. And 食糧 is preferred mainly in the context of a large scale of food supplies.
食料 includes any kinds of food. It’s a general term.