1. In a small bowl, combine onion with 2 tablespoons lime juice, 1/2 teaspoon sugar, and 1/4 teaspoon coarse salt; toss to combine. Let lime-marinated onion sit at room temperature until it softens and brightens in color, about 1 hour (up to 1 day, covered and refrigerated).

2. Make dressing: In a blender, combine remaining 1/4 cup lime juice, jalapeno, cilantro, and remaining 1 1/2 teaspoons sugar; season generously with salt. Blend until smooth. With the motor running, add oil in a steady stream through the feeder opening until incorporated.

3. Just before serving, slice avocados; arrange on a serving plate. Top with onion; drizzle with dressing.