Step 1Combine sugar, honey, marmalade and apple juice in large heavy pot. Cook over medium heat, stirring until sugar and marmalade have dissolved. Bring to boil and simmer over low heat just until it begins to thicken, 2 minutes.
Step 2Peel apples and place in bowl with lemon juice to prevent them from discoloring. Core each apple, slice and cut slices in half. Add apples to syrup in pot and toss to coat. Simmer, covered, 15 minutes; mix well. Uncover and simmer on low heat until apples are very soft, 10 to 15 minutes. Stir to prevent sticking. Transfer to a glass bowl and cool to room temperature. Cover with plastic wrap and chill in refrigerator 2 hours.
Step 1Combine flour and sugar in bowl of electric mixer. Add margarine and, starting at low speed, stir until pieces of flour-covered margarine are cut into tiny particles. Stop machine to check consistency. Add egg yolks and blend until particles are moistened, add water and blend until dough comes together. Don't over-mix or dough will be tough. Wrap in waxed paper or plastic wrap and refrigerate 5 minutes.
Step 2Remove one-fourth of dough and refrigerate. Flatten remaining dough into thin round disk and press into 11-inch tart pan with removable bottom.
Step 3On a floured board, roll out remaining one-fourth dough into 12-inch square. Using a fluted pastry cutter or knife, cut into 16 to 18 (1/2-inch) strips. Chill 10 minutes.
Step 4Spread Filling evenly in pastry-lined tart pan. Arrange 1/2 of dough strips across top of filling, spacing as evenly as possible. Arrange remaining strips in opposite direction, across first strips of dough, making a lattice pattern. Cut off strips even with edge of pan and press each strip with bottom pastry and pinch to seal.
Step 5Place tart on baking sheet and bake at 375 degrees until golden brown, 1 hour. Remove from oven and set on rack to cool. Remove from tart pan by carefully loosing bottom from sides of pan.