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?
Disclosing this would mean disclosing the same about Jamed and Peter, and I imagine he didn’t want to do that, so that they could be remembered in the best possible way.
Besides, Dumbledore took him in Hogwarts despite his condition twice - he wouldn’t want to tell him his trust was misplaced.
Excellent point about Lupin not wanting to break Dumbledore’s trust in him. Not necessarily the morally “right” thing to do, but the reasons are sound. Fortunately, it (mostly) worked out in the end, as Sirius was actually innocent.