Elle
Elle is a French actress that travels to Japan for a film job, an anti-war movie. The film, taking place right after World War II, has many war references. Elle in French simply means Her, just as Lui means Him. Elle means Lui, who is an architect, while she is in Japan for her film. The two discuss how hard the war was for them - Elle had a German lover, and Lui lost his family in the Hiroshima bombing. Elle eventually has to go back to France, and doesn't have a hard time doing so because the attachment between these two people was weakened by the effects of war.
Lui
Lui is a Japanese architect that meets Elle while she is trying out for an anti-war film in Japan. Lui was once a member of the Imperial Japanese army, and he lost his family during the Hiroshima bombing. Lui and Elle find that they can relate closely to one another because of their hard times during the war, but when Elle has to leave, it doesn't really impact either of them.
L'Allemand
Simple "The German" in French, L'Allemand was Elle's lover before the war. However, he became a German soldier, and this separated the two. Elle frequently recalls L'Allemand while she is talking with Lui, and implies that she wishes the war had never happened.