Yes, Lightroom puts keywords and other metadata in a databank, while Bridge writes it to the image.
Don't use Lightroom, but look for an opton to write metadata to image or some such wording. It is there someplace.
In lightroom, select the files you want updated, goto the menu : metadata>Read metadata from files. This will load the metadata from the file into lightroom, including the stars.
However, if you recently edit the files in lightroom and you did not save the metadata to the drive, that editing will be lost. So it is always a good idea to save the metadata to your hard drive when your done editing the file. Then any app that can read metadata can use the new information.
If you know you will not loose any editing information, you can also sync the folder. This will update all the files in that folder + sub folders.
In lightroom to save metadata just hightlight the file and hit ctrl-s. Or goto Catalog Settings>Metadata and turn on Automatically write changes into XMP file. Keep in mind that autosaving the metadata will slow down lightroom.