Preheat oven to broil. Place mushroom caps on a baking sheet, and brush with oil. Broil until soft and slightly browned.
Meanwhile, melt butter in a saucepan over medium heat. Stir in flour to make a paste. Whisk in milk; cook, stirring frequently, until hot. In a small bowl, beat egg yolks together, then pour a small amount of the hot milk mixture into the yolks. Whisk this yolk mixture into milk in saucepan. Remove from heat, and stir in 1 1/4 cups cheese.
Preheat oven to 350 degrees F (175 degrees C).
Place mushroom caps, hollow side up, in an 8 inch, round baking dish. Cover with crab, and sprinkle with lemon juice. Pour cheese sauce over mushrooms and crab, and top with remaining 1/4 cup cheese.
Bake in preheated oven for 20 minutes, or until hot and bubbly.
