Immerse six 12-inch long bamboo or wooden skewers in a dish full of water; let soak about 20 minutes.
Meanwhile, heat a large nonstick skillet over medium heat. Add the oil and leek. Cook and stir until leek is softened and a bit golden on the edges, about 4 minutes. Remove from heat; transfer half of the leek to a bowl.
Add the tomatoes to the leek remaining in the skillet. Put over medium heat, and stir in half of the garlic, the coconut aminos (or soy), cumin and red pepper flakes. Simmer until thickened to the consistency of ketchup, about 10 minutes. Remove from heat. Stir in mint, taste for seasoning, adding salt as needed. Cool.
4. Stir egg, breadcrumbs, olives, parsley, remaining garlic, lemon zest, lamb and 1 teaspoon salt into the leek in the bowl. Use clean hands to mix lightly until mixture is homogenous. Shape about 1/4 cup of the meat mixture into a log about 1 inch in diameter and 3 inches long. Repeat to make 12 sausage logs.
Run a skewer through the long ends of the logs, putting 2 on each skewer. Place the skewers on an oiled perforated broiler pan or rack set over a baking sheet. (Uncooked sausages can be refrigerated up to several hours.)
Heat oven to 400 degrees F on convection or 425 degrees F conventional. Cook skewered sausages, turning once, until the juices run clear, about 15 minutes. Transfer to a serving platter. Serve hot with the tomato sauce on the side for dipping.