Liv is indeed pronounced as "leave" and means "life".
But I guess Americans use it as a nn for
Olivia, then pronounced with a short I-sound (Livv).
Leo and
Lucy are also formal names in themselves.
Lucy is not more a nn than
Mary is a nn for
Maria.
"But it’s all right now.
I learned my lesson well.
You see you can’t please everyone
So you got to please yourself."
Rick Nelson, GardenParty
"It does not become me to make myself smaller than I am." (
Edith Södergran 1891-1923)