Four hours or less before serving, cut figs and ham slices lengthwise into quarters, making 24 pieces of each. Roll each fig quarter tightly in length of ham and secure with toothpick. Using pastry brush, paint each wrapped fig lightly with olive oil and grind a bit of pepper over the top. Cover with plastic wrap and set aside.
When ready to cook, prepare charcoal fire or preheat electric grill or broiler. Cook figs about a minute each side. They should be warmed through and just beginning to color. Transfer figs to platter and remove toothpicks. Drizzle each with a little more olive oil and a few drops of lime juice. Pass figs with fresh toothpicks and cocktail napkins.