Lee. 24, has one goal and seven assists in 35 games with the Senators this season.
Selected in the first round (ninth overall) by the Senators in the 2005 NHL Entry Draft, Lee has scored five goals and 23 assists in 167 career games in Ottawa.
He will become a restricted free agent at season's end and is currently making $875,000.
Gilroy, 27, has two goals and 15 assists in 53 games with the Lightning this season.
Signed as an undrafted free agent out of Boston University by the New York Rangers in 2009, Gilroy has scored nine goals and 34 assists in 180 career games with the Lightning and Rangers.
The 2009 Hobey Baker Award winner will become an unrestricted free agent at season's end. The Lightning signed him to a one-year deal worth $1 million prior to this season.