Lori is a variant of
Laura;
Laurence and
Laura basically mean the same thing ("laurel") so no,
Laurence isn't far off from
Lori. I quite like
Laurence. I'm a huge
Little Women fan so "Teddy/Laurie/Laurence" always have a special place in my heart. It was also the name of my great-great grandfather and his father, too.
I much prefer
Laurence over
Lawrence.
Laurence is handsome and soft yet still masculine.
Lawrence kinda irks me today; its the "w".