Yes, I believe that Lebron James has redeemed his image by returning to Cleveland. He expressed a maturity when he went home that he had not exhibited before when he went home. Of course, if the Cavaliers win it all, he will enjoy an outpouring of goodwill unlike anything he has experienced so far.
The population of people with a negative image of Lebron James was limited mostly to Cleveland residents/fans that felt he showed a lack of loyalty to his hometown when he left to play in Miami. For most people in general his image did not require redeeming. By returning to Cleveland it is likely that the mostly Cleveland based population that had a negative image of him will change their mind about his loyalty to the city/community.
Lebron James did what he should have done, and that was go back to Cleveland and try to win a championship. He has come back in full force and led the team to a possibility of that again, and this time he looks determined to make things happen in Cleveland. All fans should forgive him, as he looks like he is going to be winning them a championship very soon.
While Lebron James has done right by returning to Cleveland, he has not redeemed his image completely. Fans still have a certain amount of trepidation about going all-in on celebrating him. When a person is so quick to jump ship for a better offer, it takes time to return trust to a person.