If you are going to use two different programs to handle your metadata, then you need to have LR write XMP to the photo files (or associated sidecar files, depending on the file type). You can turn this option on in Preferences. Once the XMP is written to the photo, the next time you import the metadata from your files, the edits are included.
Advice: if you can find a way to use only one program to handle your metadata (e.g. Lightroom), then you will be much better off, and save lots of time updating metadata. Not only that, there is a possibility that using the two programs will cause some incompatibility in the metadata somewhere sometime.
To build on Paige's advice (with which I agree): The option in Preferences causes LR to write your edits and metadata changes back to the files in background. Usually, that happens very soon after you make the changes, but people have reported that sometimes with large catalogs or large numbers of changes, it can take much longer for the changes to get written back. So I recommend that after an editing session, you select all the files you've edited and do Metadata > Save Metadata To File to ensure that the changes are written back before some in Expression Media changes the file again.
(In LR 4, you can set up a Filter Bar preset or Smart Collection that will search for just thoses files that need their metadata written back.)