It looks like La Grange is pretty close to the Oak brook area. If you go up to the Butterfield Rd area from about Oakbrook west to Lombard, there are quite a few places open on Thanksgiving like Weber Grill, Mc Cormack and Schmidt, Ditkas, etc. They all seem to be open and having thanksgiving dinner too.
Here is another link although there are many not on this list. Don't know specifically about the La grange area itself.
http://myemail.constantcontact.com/Rest ... fV5HxWCNN4
Toria
"I like this place and willingly could waste my time in it" - As You Like It,
W. Shakespeare