It is not my place or anyone's place to say whether Allah will forgive you, but, inshallah, if you ask Allah sincerely for forgiveness and pledge to try to not to lie in the future, you can have hope that Allah would forgive you. Allah is merciful and it does not benefit Allah to punish us! The important thing in life is that we are trying our best and we recognize when we make mistakes.
It is said that, during the time of the Prophet (S), one of the companions was involved in a number of serious sins such as drinking, unlawful relationships with women, and even stealing. [I am not saying you are, but clearly this man had a lot of problems.] One day, he went to the Prophet (S) and told him he was doing all of these things but he could not stop all of them at once, so which one should he stop? The Prophet (S) told him to stop lying.
The man was surprised since lying seemed to be the least of his problems, but he accepted the advice and left, swearing solemnly never to tell another lie again.
However, he soon realized why the Prophet (S) had said this. For when he had a chance to steal, or drink, or do something else, he thought, "If I do this, and the Prophet (S) asks me if I did it, I will have to tell him the truth." And then he thought of how embarrassing it would be if he had to tell the Prophet (S) what he was doing. And so it wasn't long before he stopped all of these other sins as well.
I hope your arm gets better soon!
