The best research I'm aware of is a Washington Post investigation of 8,000 murder arrests. Their data journalists found that half of the arrests happened in 10 days or fewer, not 48 hours.
A Washington Post examination of 8,000 homicide arrests across 25 major U.S. cities since 2007 found that in half of the cases, an arrest was made in 10 days or fewer.
The analysis underscores what police leaders and homicide experts have
said about the passage of time working against detectives. But it also
dispels the notion of a “48-hour rule” that most cases, if solved, are
wrapped up in two days. Only 30 percent of the cases led to an arrest
within that time frame, the analysis found.
So the frequently given 48-hour rule of thumb doesn't seem very accurate, at least for homicide cases. However, a graphic further down in the Post article does show that the likelihood of an arrest declines steeply within just a few days.
Of course 'finding a lead' is an ill defined term and not necessarily the same as arresting a suspect. The Washington Post piece quotes a police sergeant who argues that 48 hours for 'identifying a suspect' isn't far off:
Evidence collection and lab tests often delay an arrest beyond a
couple days. “It’s probably more accurate to say that you had a
suspect identified in the first 48 hours,” said Sgt. Greg Van Heyst,
who supervises the Tampa Police Department homicide unit.
Ultimately one would need to come up with a clear set of criteria for what constitutes a 'lead' to accurately confirm or dispel the claim.