I remember a post on here a few years ago about someone who had tried doing this and failed. I don't remember the details but you may be able to find it if you search well.
My recollection of his takeaway was that lawyers actually didn't want a lot of the things git offered. For example, they always wanted to be using the latest version -- the abstraction of multiple branches where multiple people independently worked on things then merged them back together wasn't quite how most lawyers worked. And the other big thing was a network problem: a lawyer has to us microsoft office's version control because the opposing team is going to use it, so even if you use some better editor software it still has to be sent as a word file showing the tracked changes to the other side.
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