Where can I purchase a Louis I Kahn cafeteria tray that was once
routinely used in the Harvard college cafeterias?

You mean those beige round ones with space for a cup or glass in the middle?
And Louis Kahn designed them?   I guess one of their virtues was that
they could be stacked without orienting them  - if that was a virtue. 
I found the steel mess trays in the military to be a more civilized
solution.
Anyway,  I hope you find one.

Here is one place you could start, either by email or phone:

http://www.fas.harvard.edu/~yardops/maintenance.html

or here:

http://www.harvard.edu/administration/

Or you could call the Crimson and maybe place an ad:

http://www.thecrimson.com/