Final answer:
The provided information does not contain specific details about Chesterfield's relationship with Johnson or how he tried to regain his favor, which prevents an accurate answer.
Step-by-step explanation:
The question appears to be confusing historical figures with the information provided being unrelated to Lord Chesterfield or Samuel Johnson. Lord Chesterfield, also known as Philip Stanhope, 4th Earl of Chesterfield, was a British statesman and man of letters. However, the provided information does not contain specific details about Chesterfield's relationship with Johnson or how he tried to regain his favor. Instead, it gives context about various other historical events and figures, such as the return of Charles II to the throne of England, known as the Restoration, and the political career of Chester Arthur in the United States. Without accurate information pertaining specifically to the relationship between Chesterfield and Johnson, it is not possible to provide a detailed answer to this question. As a tutor, it is crucial to recognize when there is not enough relevant information to answer a question accurately, and in this case, I would need to request more information or decline to provide an answer.