Lee, 24, has posted a goal and eight points in 35 games this season. The ninth pick in the 2005 NHL Entry Draft, Lee has totaled five goals and 23 assists in 167 career games, all with the Senators.
Gilroy joins his third club in two years. He had two goals and 17 points in 53 games with Tampa Bay this year.
The 27-year-old and 2009 Hobey Baker Award winner has produced nine goals and 34 assists in 180 games with the New York Rangers and Lightning.