Whisk together lime juice, honey, vinegar, oil, and Sriracha sauce. Divide into 2 portions. Brush one portion over trimmed and thinly sliced pork; reserve remaining portion.
Sprinkle pork with salt and pepper. Cook in a large greased nonstick skillet over medium-high heat for 3-4 minutes or until done.
For Carrot Slaw: In a medium bowl, whisk together olive oil, vinegar and honey. Peel and grate carrots, add to bowl. Toss to evenly coat; chill until ready to serve.
Separate lettuce into leaves. Peel cucumber, cut in half lengthwise, and thinly slice.
Divide pork, cucumber, and carrot slaw among lettuce leaves. Top with peanuts and chopped cilantro; drizzle with remaining sauce.
Serve with sliced apples on the side.