Place drumsticks in a heatproof baking dish and salt drumsticks on all sides. Chill for 10 min. or up to 12 hours.
Preheat grill to medium-high. In a saucepan, mix together lemon juice, olive oil, garlic paste and leaves from 2 sprigs of thyme. Heat mixture until it starts to simmer, 1 to 2 min. Remove from heat, pour half the sauce over drumsticks and reserve remaining half in saucepan. Set saucepan aside. Turn drumsticks to coat.
Place drumsticks on grill and cook, 2 min. then turn over and cook 2 min. longer. Reduce heat to low and cook drumsticks 20 to 25 min., turning 2 or 3 times.
Set lemon halves, cut side down, on grill. Use barbecue tongs and dunk grilled drumsticks in reserved sauce, coating all sides. Return chicken to grill and cook until done, about 5 min. Transfer to a serving platter. Garnish with grilled lemons and remaining thyme sprigs.