The agency pursuing Lucky in the series premise is the FBI.
Lucky follows Luciana “Lucky” Armstrong, a professional con artist whose life collapses after a multimillion-dollar heist goes wrong. The Federal Bureau of Investigation becomes one of the forces chasing her, placing the story in the tradition of crime thrillers built around a fugitive protagonist.
The FBI is not Lucky’s only danger. She is also pursued by a ruthless crime boss, creating a two-sided chase: federal investigators want to capture her, while criminals want to recover stolen money and settle old scores. That distinction matters because the question asks for the agency, not every group after her.
A common mix-up is choosing the DEA or Interpol because the story involves organized crime, international-style intrigue, and large sums of money. However, the series’ official premise specifically identifies the FBI. Apple TV’s Lucky was created by Jonathan Tropper and stars Anya Taylor-Joy as Lucky.