How to make this sentence perfectly natural,
"The sun has not risen yet, but the sky was getting lighter."

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Everything sounds good to me, except the tenses.  If you're telling this story in past tense, you should say "The sun HAD not risen yet, but the sky was getting lighter."  If you're telling the story in present tense, you should say "The sun has not risen yet, but the sky IS getting lighter."

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It's natural with the corrected tense. It might be more common to just say 
"The sun hadn't risen yet, but it was getting lighter."

You could also express the idea more succinctly with "predawn light"

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