Preheat an outdoor grill for high heat and lightly oil the grate.
Mix lamb, shallot, mint, paprika, cumin, salt, coriander, cinnamon, black pepper, and adobo together gently in a bowl. Form lamb mixture into 8 cylinders approximately 1x3 inches in size, using about 3 tablespoons of mixture per cylinder.
Reduce grill heat to medium; transfer lamb to grill and cook until no longer pink in the center and the juices run clear, 3 to 4 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Remove from grill.
Mix yogurt, tahini, and lemon juice together in a bowl until sauce is uniform.
Spread 1/4 of the yogurt sauce down the middle of each pita; top with lamb, tomato, feta cheese, and lettuce.