Yes—based on the community answer, the practical route is to use the Facebook Graph API. Facebook stores a photo caption in the photo’s metadata field often referred to as the photo “name,” and the API can return that information for photos in an album.

In short, you would:

1. Access the album/photos through the Graph API.
2. Request each photo’s caption/name field.
3. Export the results and map them to your files for import into Lightroom.

A good way to test this is with Facebook’s Graph API Explorer before building a full workflow. Whether you can automate the Lightroom side depends on how you match the exported captions to the original image files, but extracting the caption text itself should be possible through the API.

So: likely yes, but not through a simple Facebook download tool—you’d use the Graph API to retrieve the captions programmatically.