Oooh, something I know stuff about! I love riding Amtrak routes!
He could have caught the northbound Tuesday morning around 7:30-7:45 or the southbound around 10 pm in Lafayette. Although that particular route can be well beyond fashionably late!
That particular route runs Sunday,Tuesday, Wednesday, Friday with overlap of two different routes, the Hoosier State 850/851 (Indy to Chicago) and Cardinal 50/51 (NYC to Chicago).
Lafayette doesn't have a ticket office, but they do have a kiosk. Some kiosks allow you to purchase tickets there, others just allow you to print tickets purchased online. I would imagine you can buy tickets there just because it's a college town and fairly busy. It's been a year since I've taken a trip, but I'm positive I had to show ID when boarding.