sounds better to me: Lauren.
does it sound strange with same letter? well, I personally like different first letter names for siblings because if you want to buy them personalized things you only have to buy the first letter (for example: there's a cute plush pillow at a department store that has the letter "A", who gets the pillow if both kids have the same letter? Also, there is a cute necklace with the initial "L", which daughter gets the necklace? If one sees the other wearing it, or sleeping on it, they may feel weird about it.) Just my opinion, doesn't mean I'm right ;)