Hello, sorry to hear you are having this issue. I did a little bit of research and from what I found, you can get the gif to replay by tapping on it. But no solutions as far as getting it to play on a loop. I hope this helps.
I just tried it on my Note 10+ and it was able to play it on a loop.
Does the file that you've used end in a .gif?
If unsure on how to check this: swipe up from the file while viewing it in your gallery and it'll show in the file name.
Try to download the gif and setting it up as your lock screen once again.
Hey sorry for the inconvience but the video if short enough actually plays in loop until the screen goes dark /stanby again. Check with a 1-2 sec .gif to see what I mean. Hope this helps