If I'm not mistaken, all the flag stops you listed had shelters. I will try to get some more detailed information this weekend, but I believe Cavanaugh, Cook, Springville, Hicks and possibly Lake Park were discontinued in the '60s or early '70s. Michigan Boulevard, Andry, Smith, Birchim, Saugunay, Terre Coupee, Olive and Lydick were, I think, discontinued in the early-to-mid '80s. (It should be noted that even after stops were discontinued, certain crews would sometimes stop if they knew a passenger wanted to board or alight at a certain crossing.)
By 1993, LaLumiere was the only flag stop from your list still shown on the public timetable. Between 1993 and 1994, NICTD's last flag-stop elimination program saw the end of the stops at Ambridge (Gary), Dune Acres, Kemil Road, Willard Ave. (M. City), LaLumiere, Rolling Prairie and New Carlisle. Remaining flag stops in the 1994 timetable were Clark Rd. (Gary), Miller, Ogden Dunes, Beverly Shores and Hudson Lake. In 1997, Miller and Ogden Dunes were made regular stations, leaving only the current three flag stops.
I'll try to do some research this weekend and pin down the discontinuance dates a little more closely.