It's very awkward, as double negatives usually are. Gavin's option is better, as would be To avoid making her parents angry, she didn't tell the truth.

Another option is to use anger/upset as the verb and leave out "make". "To avoid upsetting/angering her parents, she didn't tell the truth." or as a noun: "To avoid her parents' ire/anger/wrath, she didn't tell the truth."

Thanks

Not really . What you are saying makes sense, but the grammer isn't right. Try this: "She didn't tell the truth because she didn't want her parents to get upset"