I also shorten Laurence to Laurie ,but his brother and sister always use his full name as does his wife.My O.H. called him Laurie too.
He is named after a little boy who was a playmate when I was an evacuee .
He was lovely ,then whilst doing my training there was a gorgeous baby named Laurence I loved so much ,so Bonny and happy.
You were not supposed to nave favourites but he was exceptional.
Our Laurence is lovely , as I am sure your Lawrence is too.
Viktoria.