Me and my ex.?

me and my ex broke up, i lied to her, it was a small lie. and she scared i will hurt her agin with lies, she cares for me deeply, as do i her, i know i was wrong for lieing no matter how small, i lied to her not once but twice after promising i would not agin. im trying everything to prove to her i will never do it agin, but shes hurt and scared i will, like i said she cares for me deeply, how long should i try to win her back, befor i give up i dont want to give up, because i love her with all my soul, but you can only try so hard to win her back, is it possible? i will not give up on her, need advice on what iu should do.