Lagaan: A rebellious teenager must put together and train a ragtag team including a Sikh, a mute, a hairy fortune-teller, and a man with a gimp arm (who is their secret weapon), to play cricket so they can save their village from taxes that will force them all into starvation. Also, it is a Bollywood musical.
Il Mare: Woman becomes pen pals with someone whose letters take two years to reach her.
The Lake House: American woman becomes pen pals with someone whose letters take two years to reach her.
Lakeview Terrace: Cop finds out his new neighbors are an interracial couple. Racism ensues.
The Land Before Time: Five kids walk westward for a few days. All the while, their de-facto leader is following the advice of what is either a hallucination or his mother's ghost. And then they kill the guy who killed the leader's mother.
The Lego Movie: A construction worker teams up with a motley crew of heroes (including a riot grrl, an old blind man, a guy obsessed with outdated space technology, and a mix and match critter with anger-management issues) to stop a businessman from covering a city in super-glue.
Or: Maximus chases Wolverine for his entire life over some bread. Along the way, Wolverine adopts Catwoman's daughter. Borat and Bellatrix Lestrange try to rob him. Eventually, they all get involved with some students who have blocked off the roads (an action which gets a horrifying number of people shot). Nearly everyone dies, though the only really villainous character survives and thrives. It's a musical.
The Lovely Bones: A girl is murdered by Stanley Tucci, then her spirit plays around inside several Macintosh wallpapers to reach Heaven while her family deteriorates. Tucci falls off a cliff.
Lucky Number Slevin: An unlucky guy stays over at his friend's house in New York, then two gangsters try to make him commit murder and come up with a ton of money. He goes on dates with his friend's plucky neighbor.