Combine honey, lemon juice, salt and pepper to taste and water in a small bowl. Gradually whisk in 2 tablespoons of the olive oil. Taste and adjust seasoning, then set aside.
In a large bowl, toss endive and lettuce with remaining tablespoon of olive oil and sprinkle with salt and pepper to taste. Set aside. In another large bowl, toss apple, cheese and almonds with the vinaigrette. To serve, place a mound of the endive-lettuce mix on a plate, then top with a few spoonfuls of the apple-cheese mixture. Repeat for other plates and serve immediately.