Lemieux, the son of former NHLer Claude Lemieux, produced three goals and three assists in 19 games with the Rangers last season, after notching nine markers and 11 points in 44 contests with the Winnipeg Jets in 2018-19.
The 23-year-old winger was part of the package sent to New York in exchange for Kevin Hayes in a late February deal before the deadline.
Lemieux spent parts of two seasons with the Jets after being dealt by the Sabres, who drafted him 31st overall in 2014. He did not play a game for Buffalo.
Tony DeAngelo is now the Rangers' lone unsigned RFA.