The Come Fly With Me comedian declared that he was "really upset" and "disappointed" by the tweet about his former civil partner, who hanged himself in 2009.
After reading the joke from a user named 'oOfuscoOo', Lucas hit back: "Shame on you...I'm not joking. I think you should delete that tweet. It really upset me."
He added: "I'm disappointed that @oOfuscoOo thinks jokes about the suicide of my former partner are funny...I appreciate all the support on here over the past couple of years but it's time to shut down my Twitter account. Xx."
Lucas's profile is still up on Twitter, but there have not been any further tweets since his threat yesterday (February 25).
The user who upset him, however, is no longer on the site.
Lucas and McGee were married in December 2006, but the funnyman filed for divorce 18 months later, citing his partner's "unreasonable behaviour".