Lauren, Lucy, Louise Try this website, http://www.aussiethings.com.au/babynames/lgirl.htm
A sport that starts with L that girls might play in school is lacrosse. It's not particularly posh.
Leah, Lori, Lorah, Liona, Linda, Lynn, Laura, Lottie, Lucinda.
Prunella
Wanda
Isabbella
Reah
ZeldaZinniaZoeyZoeZannaZilpha
Lamborghini is a name of a foreign car from the 90s that starts with the letter L.
lemonade
London
Link from Zelda
The only name I can think of is Ursula.