We broke the story ... Lively is suing Baldoni for sexual harassment and what she claims is a coordinated effort to destroy her reputation. In the lawsuit, Blake's attorneys include text messages they recovered via subpoena -- messages they say were sent between Melissa Nathan and Jennifer Abel, two PR pros.

The New York Times published photos of the messages Nathan and Abel allegedly sent to one another ... including one in which they're apparently gloating over their comprehensive takedown of Lively.

According to the suit, Abel told Nathan that the online narrative was "so freaking good" and Justin -- presumably referring to Baldoni -- saw this as "a total success."

Nathan's alleged response ... "The majority of socials are so pro Justin and I don’t even agree with half of them lol."

Lively's team also accuses Nathan of saying she wanted "to plant pieces this week of how horrible Blake is to work with" ... even allegedly speaking to an editor at a major news organization who was "ready when we are" to run the stories.

The texts also reference a man named Jed Wallace ... who Nathan writes in one text is responsible for the success of shifting the narrative about Lively and Baldoni on social media.

Nathan even writes in one text about the people backing Baldoni over Lively ... saying it's "actually sad because it just shows you have people really want to hate on women.”

One message shows the confidence Nathan had in the strategy ... with Abel saying she outdid herself and Nathan responding, "That’s why you hired me right? I'm the best."

As we told you ... the text messages are just one part of a much larger lawsuit -- which accuses Baldoni of watching Lively while she changed, talking about his sexual exploits and even showing her a video of his wife naked.

Baldoni's lawyer, Bryan Freedman, lashed out at the lawsuit, saying the claims are "false, outrageous and intentionally salacious with an intent to publicly hurt."