Can you make frames in Lightroom?

Yes you can do this in the print module.

In the settings under Print Job select Print to: JPEG File. Select Custom Package and you should have a blank canvas. Then drag your image onto the blank page and resize as needed. Its not as robust as doing it in photo-shop, but works well enough.

and as another poster mentioned you could get this accomplished in Effects -> Post Crop Vignetting in Develop module as well, but you wont get a sharp border and can only get it black or white.  In the Print module you could select any color you want for the background.

Hope this helps!

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Liya Zlotnik
Blog: www.dumplingsphotography.com/blog