Pay attention, dear reader, for in this Levantine drama lies more than the monetary policy of a country not quite the size of Connecticut. On the surface, Mr. Salameh has earned his reappointment by providing Lebanon with the measure of economic stability that its politics notoriously lack. The country’s banks sailed through the financial crisis, and inflation has been kept in reasonable bounds. In 2009, Mr. Salameh was named central banker of the year by the Banker magazine.

But a different view of the Lebanese banking system was recently afforded by the Drug Enforcement Agency and the Treasury Department, which in February designated the Beirut-based Lebanese Canadian Bank (LCB) as a primary money-laundering concern.

The bank, which in 2010 had assets of some $6 billion, is alleged by the DEA to have facilitated the money laundering of a global drug-trafficking network linked to Lebanese drug kingpin Ayman Joumaa, who, the agency says, was moving as much as $200 million a month through the bank. The DEA also claims that LCB had ties with one Abdallah Safieddine, the Tehran-based envoy of Hezbollah, who “was involved in Iranian officials’ access to LCB and key LCB managers, who provide them banking services.”

The LCB denies the accusations, and thanks to Mr. Salameh’s efforts it is now in the process of being acquired for about $600 million by the Lebanese affiliate of Societe Generale, with blessings from the U.S. Treasury. More on that in a moment.

In the meantime, it’s worth recalling the last great Lebanese banking scandal. In July 2003 the al-Madina bank was taken over by Mr. Salameh after it came to light that the bank had a $300 million cash deficit. It soon became clear that al-Madina had sidelines laundering money for Iraqi officials and their partners as part of the U.N.’s oil-for-food scam. The FBI also discovered al-Madina was the bank of choice for a Hezbollah arms dealer who once made a deposit of $160 million to the bank—in cash.

But the most interesting revelation about al-Madina concerned its ties to the Assad regime in Syria, which at the time had its army in Lebanon. According to an exhaustive 2006 report in Fortune, Syrian officials and their Lebanese friends took a 25% cut of the $1 billion laundered by the bank. “Among the recipients of this money,” Fortune reported, “were Bashar Assad’s brother Maher” and Assad family henchmen Ghazi Kanaan and Rustom Ghazali, who took “more than $32 million from al-Madina.” Thus, for anyone who wonders, is the Syrian beast fed.

Following the February 2005 assassination of former Lebanese Prime Minister Rafik Hariri, a U.N. investigation noted that “it very much seems that fraud, corruption, and money-laundering could also have been motives” in the murder. Hariri, it seems, was intent on re-opening the al-Madina inquiry—and embarrassing the Assads—had he lived to be re-elected as prime minister. The Syrians did not take kindly to the idea: Mr. Salameh, according to Fortune, “didn’t deny reports that Ghazali had threatened him into closing the investigation.”

In 2006, following the departure of the Syrian army, the al-Madina files were transferred from the central bank to the Ministry of Justice. Two bank officials were arrested and jailed on charges of misappropriating funds; the rest of the case, including the money-laundering side, was left to languish in memory.

That, too, may wind up being the fate of LCB. If so, it will send a signal to Lebanese bankers that the price to be paid for running a dubious bank—an arranged sale to a Western bank—is small. And it will send a signal to Lebanese politicians that the West won’t ask too many questions about a banking system that itself doesn’t ask enough questions about the terrorists and tyrants who transact business there.

Fortunately, the Societe Generale takeover isn’t a done deal. Sources tell me that advisers on the acquisition have raised thorny questions about a number of suspicious accounts held by the LCB bank. Questions are even being raised in the Lebanese press about the desirability of having as a central banker a man “who can be accepted by Damascus, Washington, Paris, Riyadh and Tehran.”

Those questions should be pressed harder. Lebanon is girding for the unsealing of indictments by a U.N. tribunal in the case of Hariri’s murder, which is widely expected to implicate Hezbollah and maybe also the Assad regime. The incoming Lebanese government of Prime Minster Najib Miqati is planning a unified stand against the tribunal.

The West has staked a great deal on seeing that tribunal succeed. Applying maximum scrutiny to Lebanon’s banks is one way of reminding the country’s politicians that there may yet be a price to be paid for making common cause with Hezbollah.

Write to bstephens@wsj.com