In a small bowl, whisk together the lemon juice, vinegar, mustard, pepper, and salt. Drizzle in the olive oil in a slow, thin stream, whisking all the time until the dressing is emulsified.
Peel the avocados and cut them into segments approximately the same size as the oranges. Combine the avocados and oranges in a bowl and toss them gently with just enough dressing to coat. Mound some of the salad on each plate and scatter some mint leaves over the top. Serve immediately.
