Lochte, Feigen and two other members of the US swimming team said they had been robbed at gunpoint in a taxi in Rio.
But police say their account of when they arrived at the Olympic village does not square with CCTV recordings.
Lochte's lawyer told the BBC he got back to the US two days ago.
"He arrived back before the judge issued anything," said Jeffrey Ostrow.
"He was never asked to remain for further investigation or for any other purpose after he met with Brazilian authorities after he gave a statement."
The swimmer's Twitter account shows footage of him arriving back in the United States on Monday.
Lochte is one of the most successful swimmers in history, with 12 Olympic medals and he once had his own reality television show in the US.
In Rio, he swam in two events, winning gold in the 4x200m freestyle relay.
Feigen, who told the San Antonio Express he is still in Brazil, won gold in the 4x100m freestyle relay.
Accounts of what happened to the swimmers have been confusing from the beginning.
Lochte first told US TV network NBC about it but International Olympic Committee spokesman Mark Adams said reports of the robbery were "absolutely not true".
The US Olympic Committee (USOC) later confirmed the swimmers' accounts.
Lochte himself told police that he and team mates Feigen, Gunnar Bentz and Jack Conger had all attended a party in the French Olympic team's hospitality house on Saturday evening.
He said that during their return drive to the Olympic village, their cab was stopped by men posing as police officers.
One of the men held a gun to his head, Lochte said, and robbed him of his money and personal belongings.
But police investigating the case say they have found no evidence of the robbery. They also point to "inconsistencies" in the swimmers' accounts.
Lochte and Feigen told police they and their fellow swimmers had returned to the Olympic village at 04:00 local time (08:00 GMT).
But CCTV recordings appear to show the swimmers returning to the Olympic village at 07:00 local time.
Police say they have not been able to track down the driver who the swimmers said drove them back to the village.
They also said that Feigen and Lochte gave different accounts of how many men robbed them.
Investigators have requested a search warrant for the rooms the swimmers stayed in with a view to examining Feigen's mobile phone.
The US Olympic Committee (USOC) confirmed that Brazilian police had sought the passports and further testimony from Lochte and Feigen.
In a statement the committee said: "The swim team moved out of the village after their competition ended, so we were not able to make the athletes available."