“long deserved” means something that’s been properly earned (for a long time). You could also say “well deserved” or “much deserved” (e.g. “a well deserved nap”).

long deserved = he has deserved it for a very long time

Thanks for the comments. I've got a related question. Can you please help me with the expression "a long-deserved nap"? What does it mean here? Is there a person who "deserves" a nap? How can one deserve a nap?