Combine sugar and 3/4 cup water in heavy small saucepan. Scrape in seeds from vanilla bean; add bean. Bring mixture to simmer over medium heat, stirring until sugar dissolves. Simmer until syrup thickens and is reduced to 1 1/4 cups, about 8 minutes. Cool to room temperature. Discard vanilla bean. Transfer 1/2 cup syrup to small bowl. Whisk in 1 tablespoon lime juice. Cover lime-vanilla syrup and chill.
Mix gelatin and remaining 7 tablespoons lime juice in small bowl. Let stand until gelatin softens, about 10 minutes. Add to syrup in saucepan. Stir over low heat just until gelatin dissolves, about 5 minutes (do not boil).
Using electric mixer, beat eggs in large stainless steel bowl at high speed until mixture falls in heavy ribbon when beaters are lifted, about 6 minutes. Gradually beat in warm lime syrup. Place bowl over saucepan of simmering water (do not allow bottom of bowl to touch water); beat until thermometer registers 140°F for 3 minutes, about 5 minutes total. Place bowl over larger bowl of ice water; beat syrup mixture until cold, about 3 minutes.
Beat whipping cream in medium bowl until peaks form. Fold into syrup mixture in 2 additions. Fold in lime peel. Cover mousse and refrigerate until set, at least 6 hours and up to 1 day.
Using 2 large soup spoons, form mousse into 12 egg-shaped "dumplings," placing 2 on each of 6 plates. Spoon lime-vanilla syrup over mousse and serve.
