Lawful good oathbreaker paladin

One of my players has come up with a really interesting backstory, basically he was brought up in a cult worshipping an evil god as a paladin of that god, due to an event that happened he realised that the path he had been led down from birth was the wrong one and decided to break his oath and instead works to thwart that god.

To my mind this would be a perfect for the oathbreaker paladin class but the description for that indicates that the oathbreaker must be evil for they have done horrific things.

Now this was a character who was evil but is becoming good trying to atone for the bad his family have done, stop his god and his agents and try and live a good life. He is actually talking about writing his own treaties down which will be the opposite of everything his god believes. Therefore I think the oathbreaker class in this case should be allowed to be on the good end of the spectrum, we have said that the player will be neutral when the campaign starts and still having to consciously not slip back, there is a clear arc here where he can then find his own redemption and become good.

Is this an acceptable change to the oathbreaker class or should I be looking at pointing him to something different for the same storyline?