Not a fan at all, I think it's slimy and uncomfortable. I strongly dislike it.
Funnily enough, I know a very sweet man (older gentleman) called
Laurie, but I don't associate it with him because even though he's a
Laurence he hates his name and never goes by it. Equally I like the idea (not sure about practice) of
Laurence as a name for an elegant French woman - I imagine her all polished and frosty, so I'm not saying this hypothetical female
Laurence and I would ever be friends, but this idea of a chic ice-queen called
Laurence is cool.
And I like
Lauren.
But
Lawrence gives me the ick for some unknown reason. I think I've known the odd slimy guy named
Lawrence.
Of the nicknames,
Law *might* work. I don't find it natural but it's logical, not a stretch, it makes sense and there's no reason why it shouldn't work, it's just not a nice sound.
Lawrie makes the most sense, but
Laurence -->
Laurie just looks better written down.
Ren is too much of a stretch. I can't think of
Lawrence "
Ren" ever working unless it's something you make people use, it's just not where a lot of people's brains are gonna go.