Finely mince tender lower 3 to 4 inches of lemongrass for about 3 tablespoons. Mix with garlic, shallot, fish sauce, soy sauce, sugar, lime juice, oil, and pepper.
Unfold thighs; coat with marinade. Cover; refrigerate 30 minutes, included in prep time.
Heat outdoor grill to about 400°F with cooler indirect area; clean grate. Lift chicken; discard used marinade.
Grill 6 to 8 minutes per side until patchily browned and thickest meat at least 165°F. Move to cooler area if edges darken too quickly.
Rest 5 minutes; slice across thick folds and serve.