At the time, everyone thought that Sirius betrayed James, and murdered Pettigrew and several muggles. Lupin would have believed that he alone knew that Sirius was an animagus.
What reasons might he have had for withholding this information from the Ministry or Dumbledore? Lingering doubts/loyalty? Fear of persecution by association?
That’s an interesting question, because it shows how much of a complex character Lupin is.
Lupin lost his three only friends in the same period, that must have been traumatic to him. He probably also felt bad having abused Dumbledore’s trust during their teenage years.