In a large salad bowl, toss the arugula and watermelon. Set aside.
In a medium bowl, whisk together olive oil, lime juice, cayenne pepper and salt and pepper to taste. Add cubed avocado to the vinaigrette and toss very (very!) gently. This step prevents the avocado from browning in the salad.
Add vinaigrette and avocado to the salad bowl and lightly toss to combine. Top salad with freshly cracked pepper before serving.