2medium beefsteak tomatoes,or another plum and ripe variety, sliced, for serving
For the tzatziki
In a colander set over a larger bowl, combine the grated cucumber with 1 tsp (5 ml) salt. Let rest for 10 minutes. Rinse and dry thoroughly using a clean kitchen towel or paper towels.
Transfer the grated cucumber to a medium bowl, then add the yogurt, lemon juice, mint, and garlic. Stir to combine. Taste and season with salt and pepper to taste. Cover and refrigerate until ready to use.
For the lamb patties
In a mixing bowl, use a fork to gently combine lamb, onion, parsley, and oregano; season with salt and pepper. Gently form mixture into 16 small patties, about 3/4-inch (2-cm) thick. Grill the lamb patties on a grill pan or on the barbecue over high heat until medium-rare, 2 to 3 minutes per side.
SERVING: Warm the pita bread in the oven or on the grill; halve and fill each pita with lamb patties, tzatziki, and sliced tomatoes.
HOW TO SERVE AT HAPPY HOUR: Make lamb meatballs instead of patties and bake on a baking sheet lined with parchment paper in a 400° (200°C) oven for 15 minutes. On a large serving plate or platter, serve the hot lamb meatballs with tsatziki and mini-pitas on the side.
MAKE-AHEAD & FREEZING INSTRUCTIONS: The lamb patties can be made ahead of time and frozen raw or grilled. If frozen raw, thaw overnight in the refrigerator, then grill as instructed. If frozen grilled, thaw overnight in the refrigerator, then warm up on a baking sheet lined with parchment paper in a 300°F (150°C) oven for 10 minutes.
MAKE IT DAIRY-FREE: Substitute lactose-free Greek yogurt or plant-based Greek yogurt for the regular dairy yogurt.