Conway's seat will be taken at short notice by New Zealand's Wade Cunningham, who last drove for the team in a second entry at this year's Indianapolis 500.
Cunningham won the Indy Lights race at Fontana in 2005, his championship-winning season and the last year that either Indy Lights or IndyCar ran at the Auto Club Speedway before this weekend.
"Fortunately, Wade was available to drive for us, and we're looking forward to working with him again,” said Larry Foyt.
Cunningham will get special track time on Thursday for IndyCar president of competition Beaux Barfield and technical director Kevin Blanch to observe and make sure he is race ready.
"It's in everyone's best interest that he gets comfortable on the oval," said Barfield. "We have unlimited time today, so we'll watch him closely."