If I understand your problem in the right way, you want to say, that the project file (*.mpp) opens on one machine and the lookup table shows fine, and on other machines, the same project file doesn,t show the lookup values which are visible on the working machine, right?
And I also assume, it is a local mpp file (so not project server). Right?
For local files, all values are stores in the file itself, that means if you crate custom fields in your project file, it should be visible on any machine (same version, same patch level assumed - to exclude other issues).
Beside the file, you can create content in the global.mpt, what is the master template for all new projects. Nevertheless it should not interference (i.e. such a field is defined in the global as well as in the file itself), I would keep it in mind.
What I would do now is the following.
1.) Save the project file in XLM file format and have a look into the XML file (i.e with Office XML Notepad 2007 or any other XML viewer). This gives you a clue, if the file itself has a problem. You should search inside the file for some cryptic content. Dependent from the version you used for creating the file, it can happen that you took over some crap from earlier versions.
2.) It can be a try to replace / recreate the global.mpt file on the machine. You can just delete the file (save a copy). Project will recreate the fle with default at the next start, but all local settings will be away. You can also copy a global.mpt from one machine to another for testing. Resinstalling doesn't replace the global.mpt if it is there before.
If you find left over files from older MS Project Versions (i.e. global.mpt from 2007) you can delete them completely. During the first start of MS Project, settings from earlier version are taken over (there is a dialog during the fist start) and you can import old crap again and again.
3.) You can try to create a new file, create a view which is identical with the view of the old file (the column) and copy the task from the old one to the new one. Don't copy whole lines (what copies all the invisible fields), copy only the fields you need. Maybe you have the copy the resources first and to create the custom fields and lookup values.