Unfortunately Lightroom doesn't give the user the choice to write metadata into a raw file but instead writes it into an xmp sidecar file. I don't think Capture One can read this.
One workaround is to go via another program that can read xmp files and can then write the metadata directly into a raw file - iView can do this. Capture One can then read the metadata.
Another approach is to sync the metadata after you've worked on it in Capture One. Import the C1 TIF/JPEG file into Lightroom, then select the raw file first, and the C1-produced file, and use Sync. You will also have to cut and paste the keywords.
Another point is to question why you are using Capture One....
John