Well something I would advise is tests...lots of tests.
I would suggest that you will want to export from AEFX for the files going to the LAB.
Have the lab advised you of the file specs and type they require. eg seq tiif / tga....
I dont have an answer for you about managing the LUT but....
I did tests and used the "eyeometer" method. eg. I projected the tests up at the lab. The projector and screen were calibrated to a Kodak cinema spec
Actually I found color was not the issue of any significance.
I did find the gammas were a slight issue (easily dealt with)
Shadow detail requires concentrating on ( otherwise noise)
Highlights needed to be controlled to avoid blowing them out and away.
Premiere Pro does not have color management features. It doesn't use LUTs. After Effects does have color management features, and it can apply a LUT. Come to the After Effects forum for help with that.
Here's a paper that I co-wrote about color management using Adobe tools, including for digital cinema. I strongly recommend reading it:
Thats a nice piece of work Todd.
Just skimmed it on screen ...and its now printing out for some of my holiday reading.
As a D.P ...I am very interested in anything color / levels and display.
You could also look into Cineform. It has advanced color management tools and LUT tables.