Landini (Francesco) was a leading Italian composer of the fourteenth century. His musical style, sometimes known as ars nova (though that sounds like a job for Preparation H), features melodies buried under flowery decoration. Most of his surviving works are polyphonic songs in the Italian language, often using texts by himself and employing the patented "Landini cadence."
Lassus (Orlande de, a.k.a. Roland de Lassus, a.k.a. Orlando di Lasso, and the list goes on) was a leading Flemish polyphonic composer in the late 16th century. He is known to have written some 2,000 pieces of sacred and secular vocal music, with lyrics in French, German, Italian, and Latin. Some of his notable works include parody masses; but before you start conjuring up images of Weird Al Yankovic conducting a cathedral choir, those were sacred pieces based on tunes from secular songs. He wrote a musical setting of the Passion according to each of the four evangelists, and of the Penitential Psalms of David, which may be his greatest legacy.
Lehár (Franz) was a 20th-century Austrian composer mainly known for his operettas, most famous of which is The Merry Widow.
Leoncavallo (Ruggiero) was a verismo opera composer and a veritable one-hit wonder. Though he wrote several operas, only his first (the one-act potboiler Pagliacci) is regularly performed today, often in tandem with Mascagni's Cavalleria Rusticana. (Thanks to KFUO-FM in St. Louis, I will always hear Tom Sudholt's voice calling them "Cav and Pag" in my mind's ear.) A few numbers from his La Bohème are still performed, though the opera itself is overshadowed by Puccini's treatment of the same subject. Leoncavallo was also a significant librettist, writing the "book," as it were, for such operas as Puccini's Manon Lescaut.
Ligeti (György), whose Clocks and Clouds is on the program for next season's St. Louis Symphony, has written orchestral works with interesting titles, such as Apparitions, Atmosphères, and Ramifications. He has also written concertos, a Requiem, a famous opera called Le Grand Macabre, a set of Nonsense Madrigals, and chamber and keyboard works. By the way, try to pronounce his first name in one syllable.
Lloyd Webber (William), father of popular theatre composer Andrew and cellist Julian, was an organist who composed choral, chamber, and organ music in a somewhat Romantic style. After a period of neglect, his music is making a comeback these days, thanks in part to the Aeolian Singers.
Locatelli (Pietro) was an 18th-century composer known for his virtually flawless violin playing. His best-known works are the 24 Capriccios from his Opus 3 book of violin concertos. He also wrote concerti grossi and sonatas for a variety of instruments.
Lully (Jean-Baptiste, a.k.a. Giovanni Battista di Lulli), was an Italian-born composer who spent his brilliant career in service to King Louis XIV of France. He is known for Baroque music full of zip and verve, such as the dance movements from his operas, and for the powerful Miserere he wrote in memory of a government minister. He was a founding father of French opera, and is also famous for dying of an infection that resulted from an injury sustained while conducting his orchestra. Music can be dangerous!
Lutosławski (Witold) - I'm told that ł thingy is pronounced like a w - was a Polish composer who wrote four symphonies, a concerto for orchestra, and concertos for cello, piano, oboe and harp, clarinet, and violin. His interesting achievements include a form of aleatoric music in which specific notes are played ad libitum (i.e., at any speed, any number of times in succession) within a coordinated series of time-frames. An interesting example is shown on his Wiki page. I have heard a couple of his pieces, and they are worth exploring.
Lyadov (Anatoly) was a Russian musician whose compositions include programmatic tone poems (such as The Enchanted Lake), piano miniatures (such as A Musical Snuffbox) - lots of little stuff, but not much big. He had a highly promising talent, but not much follow-through, due to laziness and insecurity. We can thank him for Stravinsky's Firebird, which resulted when Lyadov failed to produce a ballet that had been commissioned of him. Good times.