The 18-year-old, who has started the last two matches, has signed a new deal that ties him to the club until the summer of 2015.
McGinn, who has made a total of three first-team appearances, is among three brothers who have all been Saints players. Paul McGinn recently rejoined Queen's Park on loan while eldest brother Stephen made his name in Paisley before signing for Watford.
Lennon said: "Developing our own young players has always been a vital ingredient in my role as a manager."
St Mirren host Brechin in the fourth round of the William Hill Scottish Cup on Saturday but could be without top goalscorer Steven Thompson, who went off during Tuesday's goalless draw at Ross County with a hip knock.
"He has not trained," Lennon said. "We will have to monitor the situation."