In general, LR 6 does recognize external changes to JPEG metadata. So something specific is going in in your situation. Let's first verify that On1 has actually changed the rating in a compatible way.
1. Take a sample pic and change its rating to 5.
2. In LR, select the pic and do Metadata > Read Metadata From File.
3. Verify the pic's rating hasn't changed to 5 in LR.
4. Upload the pic to Dropbox or similar and post the link here. We can then take a look at the pic's metadata closely.
A couple of things to check.
By default, I think OnOne does NOT write metadata to an original, but to a copy. The settings are in prefs. So if you rate it will, I believe, immediately write to an XMP sidecar for a RAW, which Lr would see and import if requested.
But JPEGs don't have sidecars, and it won't write to the original JPEG, so there is no new metadata for Lr to read. You can force the metadata you entered in OnOne into the JPEG, IIRC, with an "Embed Metadata" command. Try that.
Bothrobgendreauandjohnrellis had parts of the right answer.Unfortunately Ican't mark both as correct. So the correct workflow I should follow is to use On1 Browse before importing photos into Lightroom. Then all of the metadata would have shown up.
But robgendreau was right that the xmp sidecar files were created by On1 for the raw files butJPEG files don't have sidecar files. I was able to use "Embed Metadata" in On1 and then johnrellis's answer to do Metadata > Read Metadata From File in Lightroom and the star ratings appeared.