You can easily copy a gallery favorites submission and find just those photos in Lightroom. In fact, you can do this with any number of images in a gallery!
View the images in the back-end of your gallery that you'd like to filter in Lightroom. If you're looking to view a favorites submission, click the "Showing > All Photos" button in the header of your gallery, and then click the "View Favourites" option.
Select the images you'd like to filter in Lightroom. If you'd like to select all the images you're currently viewing, click the "Select All" button in the header of your gallery.
Click the "Copy Filenames" button in the header of your gallery.
Copy the filenames to your clipboard (press Command-C if you're on a Mac or Control-C if you're on Windows).
Open Lightroom and navigate to the "Grid" module (press G).
In the filter bar at the top of the grid module, click "Text." If you don't see the filter bar, click View > Filter Bar to turn it on.
Select "Filename" from the first dropdown (its default option is "Any Searchable Field").
Select "Contains" from the second dropdown (its default option is "Contains Any").
Paste in the filenames you copied into the text field (press Command-V if you're on a Mac or Control-V if you're on Windows).
Lightroom will now show you just those images!
Here's a video showing the whole process: