Why didn't Lupin tell Harry that Sirius was his godfather?

He actually thought Sirius was a serial killer who had personally killed one of his friends and had betrayed two other friends to their deaths por Voldemort. He only realised the truth when he saw Peter Pettigrew on the Marauder's Map. The knowledge that his godfather was the one responsible for the deaths of his parents was devastating to Harry when he found out por eavesdropping to Fudge, Rosmerta, and the teachers.

He didn't know that Sirius was innocent. The only people who'd known that the Secret Keeper had been swapped were the people involved who'd have to know - James, Lily, Sirius and Peter. It'd have been too much of a risk to tell more.