Where in the Constitution is the government empowered to hold the press "fully accountable for publishing and spreading lies"? The fact of the matter is that the press isn't required to be truthful. If the Founders wanted it so, they'd have written that into the First Amendment.
This is a cost of a free society.
The Constitution never protected libel and slander. An activist Court in the 60s invented a new “right” for the press.
Libel was subject to both criminal and civil penalties before Brennan gutted those laws.