How long does it take for diverticulitis lead to sepsis if left untreated?

It varies: If untreated it could take days or it could take weeks. But a diagnosis of diverticulitis should be treated promptly with antibiotics regardless of the risk for progression to sepsis.

Diverticulitis: If a diverticulum perforates the patient will be quite ill in a very short time. First the patient will have peritonitis then sepsis. This can occur very quickly once the process start.