1. Rinse lemon, slice off and discard ends, then cut fruit crosswise into paper-thin slices, and discard seeds.
2. In a 10- to 12-inch nonstick frying pan over high heat, bring 1 cup water to a boil. Add lemon and cook for 1 minute. Drain. Repeat step.
3. In pan, combine lemon and 1/4 cup sugar. Stir often over medium-high heat until liquid evaporates, 4 to 5 minutes; take care not to scorch fruit.
4. Rinse apricots, pit, and cut fruit lengthwise into 3/4-inch slices. In a 10-inch-wide (about 8-cup) round quiche dish or shallow casserole, snugly arrange apricots in a single layer. Tuck lemon pieces among apricot slices. Spoon brandy over fruit, then sprinkle evenly with remaining 1/4 cup sugar.
5. Bake in a 450° oven until fruit edges are tinged with dark brown, 25 to 30 minutes.
6. Stir apricot jam to soften; dot evenly over fruit.
7. Return dish to oven and bake until jam is bubbling, about 5 minutes. Spoon portions onto plates.