In a small bowl, whisk together olive oil, Dijon mustard, lemon juice, and apple cider vinegar. Add salt and pepper to taste, blending until smooth. Set aside.

In a large mixing bowl, combine white radish wedges, watermelon radish slices, chopped cilantro, and chopped red onion. Mix gently.

Drizzle the dressing over the salad and toss until evenly coated.

Garnish with fresh basil leaves and lemon slices. Serve immediately or let sit for a few minutes.