Again, you're making statements as if they were facts when they are highly contestable. You say they "lied", but as I've laid out above, the facts we know support the perceptions that were at the heart of the story told by Lochte.
They were in the cab ready to leave the station, they were removed at gunpoint from the cab, they were extorted/demanded to hand over all of their money to cover the costs of the damage (a torn poster and peeing outside), one of the athletes had to pay a big "donation" to retrieve his passport, etc.
The "lie", to the extent you can call it that, was Lochte claiming that the security guards pretended to be police when they were not. Understandable confusion, given their uniforms, their use of guns, and their threat to call in the real police.
I note that you ignore the panoply of violence surrounding this incident which provided an incentive for the Brazilian government to scapegoat Lochte and co to deflect attention from some very real crime issues during the Olympics.
The far bigger issue here is how the IOC, the band of media that cover the Olympics for a living, and the Brazilian government all glossed over the issues of abject poverty and the resort to violence in the Favelas surrounding the Olympic Village. It was an opportunity for transparent reporting of need and poverty and desperation, and was whitewashed with the bullshit demonization of Lochte and co for public urination and tearing a poster off a wall. As if his/their acts were serious crimes, especially when compared to the robberies at gun or knife point, or the stoning of Olympic buses. Sheesh.
The story propagated by Brazilian officials and Olympic officials and reporters is disinformation. The facts that they agree to do not align with their narrative.