Yes lying to the FAA is bad, and yes the FAA does give paddelings.... but the odds of a federal DOJ investigation into a PPL for a medical? I can't see much coming from this unless OP really plays his cards wrong.
Just a sampling. And it's the DOT OIG that investigates, not the DOJ. The OIG turns their investigation over to the DOJ to prosecute.
May 10, 2021
California Man Sentenced for Making False Statements to FAA
On May 10, 2021, the U.S. District Court for the Northern District of California sentenced Gregory Chrisman to 12 months of probation, a $9,000 fine, and a $200 special assessment. On November 14, 2019, Chrisman pleaded guilty to two counts of making a material false statement to the Government. The investigation revealed that on December 10, 2017, and June 24, 2018, Chrisman falsely stated that he never has and does not currently receive medical disability benefits on an FAA form, despite having received service-related medical disability benefits from the Department of Veterans Affairs (VA) since 2011.
February 2, 2021
Pilot Charged With Making False Statements to FAA
On February 2, 2021, the U.S. Attorney for the District of Utah charged Sean Naylor, a commercial airline pilot, with making false statements to FAA. On September 30, 2015; April 19, 2016; and March 6, 2017, Naylor allegedly fraudulently indicated on his FAA Applications for a Medical Certificate that he had not been diagnosed with and had never had a mental disorder of any sort. However, he received a diagnosis of post-traumatic stress disorder from a board-certified psychiatrist in July 2015.
July 28, 2020
Former California Pilot Convicted and Sentenced for Lying to FAA
On July 28, 2020, the U.S. District Court for the Northern District of California convicted and sentenced Walker Grant to 36 months’ probation, a $500 fine, and a $50 special assessment. Grant, a former pilot, pleaded guilty to making false statements about his veteran’s benefits on Federal Aviation Administration (FAA) airman medical certification forms. FAA uses the airman medical certification process to evaluate whether pilots are mentally and physically fit to fly.
The investigation revealed that Grant submitted falsified medical records to FAA in order to obtain his airman medical certificates. He falsely stated on both applications that he had never been diagnosed with and did not then or previously have a mental disorder of any sort. He also denied the existence of medical conditions for which he was receiving disability benefits from the Department of Veterans Affairs (VA). In April 2020, FAA revoked Grant’s airman’s certificate.
January 14, 2020
California Pilot Convicted of Making False Statements to FAA
On January 14, 2020, in the U.S. District Court for the Northern District of California, Nicholas Beyer was convicted of making false statements to FAA on pilot medical certification forms. A U.S. district judge handed down the verdict following a bench trial.
Evidence at trial showed that Beyer made false statements on applications for an airman medical certificate, FAA Form 8500-8, that he submitted to the Agency in 2016 and 2018. FAA uses the airman medical certification process to evaluate whether pilots are mentally and physically fit to fly. Based on the evidence, Beyer falsely stated on both copies of Form 8500-8 that he had never been diagnosed with, did not have, and had never had a mental disorder of any sort, which was not accurate. The evidence also showed that Beyer falsely stated on the forms that he was only receiving disability benefits from the Department of Veterans Affairs (VA) for knee and back injuries, when he was also receiving benefits for a major depressive disorder.