Armstrong admitted in 2013 he used performance-enhancing substances when he won seven Tour de France races.
Trump's order doesn't specifically mention Amazon, but he's accused the e-commerce giant of taking advantage of the USPS.
The United State Postal Service is expecting to ship hundreds of thousands of packages between now and Christmas Eve.
On Saturday the Postal Service will observe Veteran's Day by closing all post offices.
A former mail carrier who pleaded guilty to opening mail without lawful authority was sentenced to two years probation in federal court Tuesday.