Questions immediately facing US authorities include how to best assist the three Olympic athletes still in Brazil, stripped of their passports and now under repeated questioning from police. Eventually, officials at the State Department may also be forced to decide whether or not to return Lochte -- who returned to the United States this week -- to authorities in Brazil for questioning.
Experts say the case is unlikely to become to a bitter, drawn-out extradition fight. But larger, more complex issues are also at play, exposing long-simmering assumptions about each country that have been exacerbated by an Olympics beset by stumbles.
The swimmers' initial story seemed to validate Rio de Janeiro's well-earned reputation for violent crime, confirming for some their skepticism at the decision to host the games there. The allegation the robbery claim was falsified turned that narrative around, tapping into the perception among some Brazilians that certain foreigners use a crime-ridden city as cover for misdeeds of their own.
"It reinforced negative stereotypes Americans have of Brazil, of violence, and negative stereotypes Brazilians have of the US related to arrogance," said Paulo Sotero, the director of the Brazil Institute at the Wilson Center in Washington. "These are entitled young men that were doing something they prefer not to share with their mothers."
The US and Brazil, the respective power centers of North and South America, have endured diplomatic rough patches in recent years, including over revelations the US was routinely spying on top Brazilian officials
. Experts suspect a desire by both governments to improve ties could help mitigate the fallout from the controversy involving the US swimmers.
On Thursday, US officials downplayed any diplomatic concerns, saying the matter was for the swimmers and Brazilian police to resolve.
"This is an issue for the parties to talk about and not for the State Department," said John Kirby, the State Department spokesman. "We take the safety and security of Americans citizens abroad very seriously."
To those ends, consular officials from the US embassy were at the airport when Brazilian authorities removed two US swimmers, Jack Conger and Gunnar Bentz, from their flight Wednesday as they prepared to leave the country and seized their passports. The pair were questioned and released, but the US Olympic Committee told CNN they expected further examination of the two athletes on Thursday.
Fernando Veloso, chief of civil police in Rio, said Thursday that there was no robbery
An attorney for Lochte, Jeff Ostrow, brushed off suggestions of conflicting stories, saying the four swimmers' accounts "are 95% consistent."
Rio authorities say they want to question Lochte as well, but since he hasn't been charged with a crime, no attempts to pressure the US government to extradite him to Brazil are underway.
Even if Lochte was charged, legal experts say it's unlikely he would be forcibly returned to Brazil.
"It really all depends on how much the US government and Lochte want to cooperate," said Steve Vladeck, a CNN contributor and professor of law at the University of Texas. "We have an extradition treaty with Brazil, so there's a formal process for the Brazilians to go through if need be, but that can take months (if not years), versus some kind of more informal resolution."
A key factor in the decision: whether Lochte's statement to the police that he was robbed at gunpoint was sworn. The treaty between the US and Brazil includes only a specific list of crimes that could lead to extradition, and it doesn't include filing a false police report.
However, perjury does apply, meaning if Lochte delivered his police report under oath, an extradition request could be filed. But that request requires the approval of multiple US government actors, including at the State and Justice Departments, and would likely take months.
"I don't think this rises to the point where he's going to be extradited. This is filing a false police report, and it's being investigated as we would investigate it here," said Art Roderick, a CNN law enforcement analyst.
Less clear is how Brazilian authorities will deal with the US swimmers who remain in Brazil. The crime of filing a false police report or lying to officials carries a lengthy prison sentence, and with their passports pulled, it doesn't appear likely Conger or Bentz will return to the US soon.
State Department officials said they were barred from speaking about the swimmers' case specifically. But a US official said that, "generally speaking, when a US citizen is detained overseas, we immediately seek to meet with them, confirm their well-being, contact friends or family members on their behalf, and ensure they are treated fairly according to local laws."
"While in a foreign country, a US citizen is subject to that country's laws and regulations," the official added.