Heat grill to medium-low.
In a large bowl, combine the jam, vinegar, ginger, cayenne, and 3/4 teaspoon salt. Set aside 1/4 cup of the mixture. Add the chicken wings to the large bowl and toss to coat.
Lightly oil the grill and cook the chicken, covered, turning occasionally, until cooked through, 25 to 30 minutes. During the last 10 minutes of grilling, baste the wings with the reserved jam mixture.
In a small bowl, whisk together the oil, pesto, and lemon juice.
Divide the lettuce among individual plates and drizzle with the pesto vinaigrette. Serve with the chicken wings.
Technique: If you don't have access to a grill, you can cook this dish in the broiler on a sheet pan for the same amount of time. (Most grill pans aren't large enough to hold all the wings at once.)