Brush inside of trout with oil.
Combine shallots and next 5 ingredients; spoon evenly into trout. Place lemon slices and thyme sprigs on stuffing and outside of fish; tie trout with string. Brush outside of trout with oil.
Cook, covered with grill lid, over medium-high heat (350° to 400°) about 8 minutes per side or until fish flakes easily with a fork.