ご質問ありがとうございます。
「大げさに言う」はexaggerateと言います。「嘘にならない程度に」はso that it doesn't become a lieと言えますが、Tomoko様の日本語を訳すとonly enough so that it doesn't become a lieとかonly enough so that it isn't a lieというonly enoughをつける必要があります。
例文:Exaggerate only so much that it doesn't become a lie.
例文:Exaggerate only enough so that it isn't a lie.
ご参考になれば幸いです。