The lawyer, Joseph Bondy, asked for the appointment of a special prosecutor from outside the Department of Justice to oversee the case.
A Justice Department spokeswoman declined to comment.
The "real damage" that Bondy cited in the letter is what he describes as a delay in the production of discovery material in the Parnas indictment, which Bondy says left his client unable to deliver documents in a timely manner to comply with a subpoena issued by House of Representatives as part of its impeachment investigation, and therefore meant that Parnas could not be properly assessed as a potential witness.
Bondy does not specify how Barr's alleged conflict of interest may have contributed to any delay in the discovery.
A spokesman for the Manhattan prosecutor's office in the United States, which is suing Parnas, declined to comment.