The request comes after Lively filed an amended complaint with "significant additional evidence and corroboration of her original claims," per her lawyers

Blake Lively is seeking the communications to "expose the people, tactics and methods that have worked to 'destroy' and 'bury' her reputation," said her lawyers

Baldoni's attorney Bryan Freedman alleges in a statement obtained by PEOPLE that Lively also made 'threats to take over' their movie 'It Ends with Us'