Whisk yogurt, lemon juice, oil, ginger, garlic, garam masala, cumin, coriander, paprika, salt, and cayenne. Cut two shallow slashes across each thigh; coat with marinade.
Cover; refrigerate 2 hours, included in prep time. Heat outdoor grill to about 400°F with direct and indirect areas; clean grate.
Lift chicken, letting excess drip; discard used marinade. Cover and grill over indirect heat 25 to 30 minutes, turning once.
Grill over direct heat 3 to 5 minutes per side until patchily browned and thickest meat 175 to 185°F. Return to indirect heat if darkening before centers are ready.
Rest 5 minutes; serve one thigh per person.