Cut off the top and bottom of the lemons to expose the pulp. Cut in half lengthwise and make a V cut into each half to remove the central membrane. Nudge out any remaining seeds, and slice each half crosswise as thin as possible.
Put the lemon slices in a 3-quart saucepan with the vermouth, sugar, bay leaves, mustard seeds, and 1 tsp. salt. Bring to a simmer over medium heat, stirring until the sugar dissolves. Simmer for 5 minutes.
Meanwhile, peel the pears and cut in half lengthwise. Core, then cut crosswise into 1/8-inch-thick slices. Stem the figs and cut into sixths. Add the fruit to the saucepan and bring to a boil over medium-high heat. Adjust the heat and cook at an active simmer, stirring occasionally, until the fruit is tender and the juices are reduced and syrupy, 30 to 45 minutes. Remove the bay leaves, stir in the Dijon mustard, and cool. Refrigerate in a covered container overnight. Bring to room temperature before serving.
Photo: Scott Phillips