These names are from a list of 6000 names given to Finnish children (aged 1 to 10 years old). Some of the names may seem ordinary to Anglophones, but in Finland they're still considered rare and/or unique.
Labiba
LahjaLaina - also means "loan" in Finnish
LalitaLanaLanda
LaniLaraLarissaLauha - means "mild" (weather) and "hair grass" in Finnish
Launa
Leah / Leea
LeannaLédaLeeLeeni
Leia / Leiah / Leya
Leilah /
Lejla /
LeylaLeinikki - means "buttercup" in Finnish
Lemon
LempiLempi-Ellen
Lempi-Helmiina
Lempi-Lumia
LenaLeneLeniLenita
Lenja
Lenne
Leona / Leonna
LeonieLeonoraLetitiaLexi /
LexieLiLia / Liia
Lia-Marie
Liana / Lianna
Lidia / Lidiia /
Lidiya / Liidia
Lieko
Liia-Maria
Liida
Liila
Liilia /
LiliaLiina /
LinaLiina-Kaisa
Liina-Maija
Liine
Liinu
Liinu-Rea
Liisabel
Liisa-Lumia
Liisa-Mari
Liisbeth
LiisiLiivia /
LiviaLilaLiliLilian
Liliella
Lilja-Felicia
Lilja-Julia
Lilja-Lumia
Lilja-Maria
LillaLillan
Lilli /
Lilly /
LilyLilli-Kristiina
Lilli-Marja
Lilli-Sofia
Lilly-Maj
LiloLily-Emilia
Linda-Mari
LindsayLindvi
LineLinea / Linéa /
LinnéaLinett
LinnLinne
Linne-Lotte
Linne-Maria
Linni
LisaLisa-Marie
Lisa-Marja
Lisandra
Lisbet /
LisbethLiselottLiselotta
Liset / Lisete /
LisetteLisette-Sandra
Lisse
Lissu
Lithea
LivLiva
Livian
LizaLiza-Elmina
LizetteLohitha
LolaLorenaLoriannys
Lorika
Lorisa
LornaLotta-Hiitta
Lottaliina
Lotta-Lyydia
Lotta-Maria
Lottapeppiina
LotteLotti
LouhiLouisa /
LuisaLouise
Louizar
LounaLouna-Louise
Lova / Lowa
Lova-Li
Lovis
Lowisa
LuciaLuluLumea
Lumena
LumiLumia
Lumiana
Lumihelmi / Lumi-Helmi - means "snow pearl" in Finnish
Lumi-Jolanda
Lumikki - Snow White's Finnish name
Lumikukka / Lumi-Kukka - means "snow flower" in Finnish
Lumilia
Lumililja / Lumi-Lilja - means "snow lily" in Finnish
Lumi-Maria
Lumina
Luminea
Luminka
Lumituuli - means "snow wind" in Finnish
Lumi-Tuulia
Lumo - means "charm" and "enchantment" in Finnish
LunaLuna-Leena
Lusiina
Lycke /
LykkeLydia /
LyydiaLyydi /
LyytiLyyli
Lyylia
Lyyli-Maria