Game 4 of the American League Division Series was originally scheduled for Monday afternoon, but it was postponed until Tuesday because of rain in the forecast.
Jose Urquidy had been Houston's scheduled starter for Monday's game, but manager Dusty Baker instead will look to close out the series with McCullers, who was dominant in Game 1 while holding Chicago without a run in 6 2/3 innings.
The Astros lead the best-of-five series 2-1.
La Russa said Lynn or Lucas Giolito would start a potential Game 5 Wednesday at Houston depending on how things go Tuesday.
The Associated Press contributed to this report.