Earlier quoted context omitted.
I'm curious to know what would change your mind? The word lying means an intent to deceive, not just to state something falsely. Being wrong and stating a falsehood vs lying are very different. So maybe try to be your own devil's advocate, and see if you could see how The Federalist could be accused of lying and be unwelcome on someone else' platform.
If the media were simply repeatedly mistaken, with no bias or intent to deceive, their errors would tend to happen in both directions. The Federalist cited quite a few falsehoods that favored the left. Perhaps you could cite some that favored the right? Edit: Excluding the few right-wing media outlets, because it's quite obvious to everyone that The Federalist wasn't talking about them here.
https://www.seattletimes.com/seattle-news/politics/fox-news-...
Someone had to open the images in photoshop, alter them, and then upload them to a website. This isn't a simple lie of omission or a mistake, this is manufactured content to push a right-wing narrative.
Fox News consistently pushed the right-wing line that Coronavirus is a hoax until they were threatened with a lawsuit
https://www.youtube.com/watch?v=ifKbwDf51bA
While they were publicly telling their viewers that the virus was a hoax, internally they were implementing remote work and disease control.
Here's a giant list of the ways they've supported conservative political goals while actively working against the left, with citations and source material in the footnotes