Preheat a grill on medium-high heat.
In a small bowl, mix together the olive oil, garlic, lemon juice, salt and pepper. Rub the lamb with the garlic oil on and let marinate for 30 minutes in a large casserole dish at room temperature.
In a medium-sized bowl, add the tomatoes, shallot, jalapeno, sugar, vinegar, soy sauce, salt and pepper, to taste.
Add the olive oil, shallots and herbs to a small bowl and season with salt and pepper, to taste.
Arrange the lamb on the grill rack. Grill the lamb, covered, until an instant-read thermometer inserted into the meat registers 130 degrees F for medium-rare, turning occasionally, about 25 minutes. Remove the lamb to a cutting board and let rest 10 minutes before slicing. Thinly slice the lamb.
To assemble, put some of the chimichurri on each pita. Add some lamb and some tomato relish. Top with more chimichurri and wrap in foil or parchment paper to serve.