For the lemongrass, trimmed off the bottom end and the mostly green upper part of the stalks. Peel off a few tough outer layers. Pound the lemongrass with a rolling-pin or meat tenderizer for a couple of times. Finely minced.
In a small bowl, combine the marinade ingredients. Transfer to a large Ziploc bag.
Rinse and dry the chicken with paper towels. Place them in the Ziploc bag with the marinade and coat the chicken really well. Seal the bag and transfer to the fridge. Marinate for 24 hours.
For the pickled vegetables, in a medium bowl, combine the carrot and daikon. Sprinkle with ¼ teaspoon of salt and ½ teaspoon of sugar. With your hands, mix everything together until the vegetables are soften, about 3 minutes. Rinse under cold water and drain. Transfer to an airtight glass container.
In a medium heatproof bowl, combine the remaining sugar, white vinegar, and warm water. Stir and mix until the sugar has dissolved. Pour over the vegetables. Let it brine in the fridge for at least 1 hour before using.
30 minutes before grilling, remove the chicken from the fridge. Wipe off the marinade from the chicken. Discard the remaining marinade. Place the chicken thighs on a plate.
Preheat the grill over medium heat, lightly grease the grill with oil. Grill the chicken, skin side down for about 2 minutes, and then rotate the chicken 90 degrees to create the crosshatch pattern. Grill the chicken for another 2 – 3 minutes. Flip the chicken and grill for another 4 – 5 minutes with lid on or until cooked through. Transfer to a large plate. Cover with foil and let it sit for 5 minutes. Transfer the chicken to serving plates. Sprinkle with minced cilantro. Serve with steamed white rice, pickled vegetables and lime (if using).