1. Rinse lemon grass. Cut off and discard tough tops and root ends; peel off and discard tough outer green layers of stalks down to tender white parts. Finely chop enough to make 1/4 cup.
2. Rinse kaffir lime leaves. Stack three or four leaves at a time and cut crosswise into very fine shreds.
3. In a bowl, mix lemon grass, kaffir lime leaves, crab, shallots, carrot, cilantro, mint, and green onion. In a small bowl, mix lime juice, chili paste, fish sauce (but not salt, if using), and sugar.
4. Just before serving, stir lime-juice mixture into crab mixture. If not using fish sauce, add salt to taste. Rinse cucumber and cut crosswise into about 24 rounds about 1/4 inch thick. Top each slice with a scant tablespoon crab mixture.