Blake Lively‘s attorneys allegedly tried to force Taylor Swift into publicly supporting Lively in her beef with Justin Baldoni by threatening to release Taylor’s private text messages if she didn’t play ball … at least according to Baldoni’s lawyer.

In new legal docs obtained by TMZ, Baldoni’s lawyer Bryan Freedman claims the subpoena he sent to lawyers for Taylor was intended to get information related to possible witness tampering and evidence spoliation.

Freedman claims he has it from a good source that Blake allegedly requested that Taylor delete their text messages.

What’s more, Freedman claims one of Blake’s attorneys, Michael Gottlieb, contacted an attorney who represents Taylor and demanded that Taylor release a statement of support for Blake, intimating that if Taylor refused to do so, private text messages of a personal nature in Blake’s possession would be released.

Justin’s lawyer also alleges one of Taylor’s reps addressed the “inappropriate and apparently extortionate threats” in at least one written communication sent to Blake’s attorney, Gottlieb.

Freedman says it’s these alleged communications that he’s trying to get his hands on via the subpoena … and he says it would be evidence of “an attempt to intimidate and coerce a percipient witness in this litigation.”

For her part, Taylor’s camp has blasted the subpoena … claiming she was minimally involved in the drama on the set of “It Ends With Us” … which sparked the nasty legal war between Blake and Justin.

As we first told you … Blake and Taylor’s friendship was fractured after a text surfaced where Blake told Justin she was Khaleesi from “Game of Thrones” and husband Ryan Reynolds and Taylor were her “dragons.”

Taylor was royally pissed over the text message, and sources close to her pushed back on the notion she was ever one of Blake’s “dragons.”

Blake is trying to quash the Swift subpoena … but Freedman says it’s very relevant to the case.