The 32-year-old Lombardi, who joined New York on Wednesday, had 20 goals and 30 assists in 46 games with Geneve-Servette in Switzerland. He led the team in goals and assists, and tied for sixth in the league in goals.
In 536 NHL games over nine seasons with Calgary, Phoenix, Nashville, Toronto, and Anaheim, Lombardi has 101 goals, 161 assists and 293 penalty minutes.
He had four goals and four assists in 28 games with Phoenix and Anaheim during the 2012-13 season. He has reached 40 points three times and has tallied at least 14 goals in five of seven seasons in which he has played 55 games.
Lombardi has recorded three goals and 13 assists in 40 NHL playoff games.