Do you have a Mac with Mac OS 10.11 or newer?
If you download download you iCloud Photos to a Mac with the Photos.app on a Mac, you can use "File > Export > Export unmodified original" to save the Live Photos as pairs of JPEGS and videos. Or simply save the complete Photos Library on an external drive. Both will save the Live Photos.
I don't know, what you could do on a windows PC.