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It's saying that I should be free up some more space, that it doesn't have enough space to download the pictures, but my phone has more than 2 GB free
I assume you are getting this message on your phone. Do you have premium Lightroom or a free version of the app? What steps are you taking to "download edited photos"? Have you tried exporting an edited photo?
2 GB of free space isn't very much - how many pics are you trying to download? Are they RAW?