Katniss Everdeen's version of "The Hanging Tree" in The Hunger Games: Mockingjay - Part 1 was inspired by Lucy Gray's song, with some changes made to inspire rebels.

Source: https://screenrant.com/hunger-games-ballad-songbirds-snakes-hanging-tree-katniss/

Then Lucy learns Snow is a man who murdered three and so flees; the Mockingjays in the treetops echo her singing "The Hanging Tree," taunting Snow like a ghost.

Source: https://www.slashfilm.com/1453307/the-ballad-of-songbirds-snakes-secret-meaning-hanging-tree/

Those eagerly awaiting The Ballad of Songbirds and Snakes can finally listen to the original version of 'The Hanging Tree' song.

Source: https://www.cbr.com/the-ballad-of-songbirds-and-snakes-receives-a-new-hanging-tree-song-rendition/