I suggest that you use Photo Mechanic's Update IPTC/XMP command located in the Tools menu so that the XMP sidecar files get updated with the rating information.
In Lightroom, make sure that you're not applying a metadata preset to the images on import (menu: Metadata > Edit Metadata Presets). You may need to have LR re-read the metadata, after updating the IPTC/XMP in PM, by right-clicking on the folder from LR's Folders navigator panel and choosing Synchronize Folder from the contextual menu.
I hope this helps,
Jerry