BY CHRISTINA BINKLEY

With a little help from Gucci and Leonardo DiCaprio, Los Angeles is planning to have its own Met Ball this weekend.

New York's Metropolitan Museum of Art uses its Costume Institute Gala, which has grown into an Oscar-style evening of star-gazing and fashion, to raise its profile—and millions of dollars.

Now the director of the Los Angeles County Museum of Art, Michael Govan, hopes to raise the stature of Lacma, as the museum is known, with a red-carpet fashion event. The museum aims to be—like the Met—a broad collection of art and artifacts, including clothing, furnishings, film and other items ...