In a shallow bowl, whisk together lemon juice, Worcestershire, garlic, spices and oil. Add onion and meat, season with salt and pepper, turn to coat and refrigerate overnight or several hours.
Thread meat and onions on metal skewers.
For the Tzatziki, drain salted cucumber or zucchini for 20 minutes and press gently to squeeze out any excess liquid. Place in a bowl and combine with yogurt, lemon juice, garlic, cumin and dill; adjust salt to taste.
Heat a cast-iron grill, griddle or skillet over medium-high heat. Spray skewered meat with olive oil spray and grill until charred outside but pink in middle for lamb, 7-8 minutes, or cooked until just opaque for pork or chicken, 9-10 minutes.
Remove meat from skewers and arrange on a platter with pitas and veggies. Serve Tzatziki alongside.