Layn -- to chant the Torah or Haftorah in synagogue, using the trop (cantillations).
L'Chaim- "To Life" a traditional toast, also an engagement party (see vort)
L'illui Nishmas – It should be "a light" for the soul, this is a phrase meaning that when something is done in the merit of a deceased person's memory, their soul lights up or attains extra merit in shamayim.
Levi - member of a special group of Jews, who used to care for the Temple in Jerusalem
Litvish – A stream of orthodoxy, originating in Lithuanian, frequently followers of the Vilna Goan, aka the GRA
Londsman - compatriot; fellow Jew
Loshon - Language, lit. "tongue." e.g. Loshon Hakodesh, the Holy Language (Hebrew), Mama Loshon, Mother Tongue
Loshon Hora- badmouthing; gossip. No dancing involvedL'sameach chatan v'kallah - gladdening the bride and groom; an important mitzvah
Lulav- a palm branch, used in the service for Sukkos