There is nothing wrong with the name Lynne. The only names that the Catholic Church prohibits are those that are insulting to Christianity. There is nothing insulting about Lynne, but I would recommend using a Christian name (e.g. biblical name, saint's name) for the middle name.
Lynne Brimley's birth name is Lynne Bagley.
Shelby Lynne's birth name is Shelby Lynne Moorer.
Lynne Frederick's birth name is Lynne Maria Frederick.
Lynne Cheney's birth name is Lynne Ann Vincent.
Lynne Topping's birth name is Lynne Edea Topping.
Lynne Spears's birth name is Lynne Irene Bridges.
Lynne Pope's birth name is Patricia Lynne Parker.
Erica Lynne Marszalek's birth name is Erica Lynne Marszalek.
Lynne Margulies's birth name is Lynne Elaine Margulies.
The name Lynne can be short for Lynnette or Linda. However, being called Lynne myself, some aren't abbreviations of a name. Lynn is more popular, as Lin as less popular to Lynne.
Lynne Perrie's birth name is Jean Dudley.
Mike & Lynne