The plan is for the Cubs starter to throw 60 pitches, which is 15 less than the original pitch count.
"I'd like to [throw in a major league game after Wednesday] if I'm throwing the ball fine," Lilly said Monday. "If the club feels I'm ready to come here, then I would like to.
"But I don't care how many it takes, when I get here I want to be ready to productive."
Lilly threw 25 pitches in a side session Monday at Wrigley Field before the Cubs' home opener against the Milwaukee Brewers.
Indications are he'll throw one more minor league start after Wednesday to get his pitch count to 85 before joining the major-league team.
At this point, Lilly is on track to pitch April 24 at Miller Park, if he stays on an an every five-day routine without a setback.
Bruce Levine covers baseball for ESPNChicago.com.