Preheat oven to 400°. Grate 1 teaspoon lime rind; squeeze 1 1/2 tablespoons lime juice over a small bowl. Combine 1 tablespoon juice, 1/2 teaspoon rind, and chutney in a medium bowl. Cook rice according to package directions, omitting salt and fat. Stir in onions, 2 tablespoons chutney mixture, 1 1/2 teaspoons juice, 1/2 teaspoon rind, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Sprinkle pork with 1/4 teaspoon salt and 1/8 teaspoon pepper. Heat a large ovenproof skillet over medium-high heat. Coat pan with cooking spray. Add pork to pan; cook 4 minutes, browning on all sides. Place pan in oven; bake at 400° for 10 minutes or until thermometer registers 155°. Spoon 1/4 cup chutney mixture over pork. Cover loosely with foil; let stand 5 minutes or until temperature reaches 160° (slightly pink). Cut pork into thin slices; serve with rice.