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?
It’s been too long since I last read it, but I think it felt more like he didn’t want to do further harm. Sirius was his friend before and the perceived betrayal did change that but not momentarily, I think.