Drain yogurt in a paper-towel-lined sieve set into a bowl in refrigerator, discarding liquid occasionally, 8 hours, then transfer to a clean bowl.
Sprinkle gelatin over 1/4 cup milk in a small bowl and let stand 1 minute to soften.
Scrape seeds from vanilla bean pod into remaining 3/4 cup milk in a 1-quart heavy saucepan, then add pod, sugar, and zest and bring to a simmer over moderate heat, stirring until sugar is dissolved. Stir in gelatin mixture until dissolved.
Pour through a fine-mesh sieve set into a metal bowl, discarding solids, then set bowl in a larger bowl half-filled with ice and cold water and let stand, stirring frequently, until cool, about 10 minutes.
Add milk mixture gradually to yogurt, whisking. Beat cream with an electric mixer at high speed until it just holds soft peaks, then fold into yogurt mixture gently but thoroughly. Chill mousse, covered, folding twice in first 20 minutes, until set, about 2 hours.
Scrape seeds from vanilla bean pod into a 2-quart heavy saucepan, then add pod, sugar, water, apricots, and 1 teaspoon lemon juice and cook, uncovered, over moderate heat, stirring frequently and skimming off any foam, until fruit is tender, 8 to 12 minutes. Cool to room temperature, about 30 minutes.
Add lemon juice to taste and discard pod.
Serve sauce topped with mousse.
· You can substitute 1 1/2 cups Greek yogurt for the whole-milk yogurt. (Do not drain Greek yogurt.)· Mousse can be made 1 day ahead and chilled, covered.· Sauce can be made 3 days ahead and cooled completely, uncovered, then chilled, covered. Bring to room temperature before serving.
