Cut one lemon in half, and each half into 6 wedges. Then cut the wedges crosswise so that you have 24 small pieces of lemon. Pick out any pits. Zest the other lemon and squeeze and strain the juice; you should have about 1 1/2 tablespoons juice.
In a medium-sized bowl, combine the yogurt, shallots, salt and pepper, and the lemon zest and juice. Transfer half the marinade into another medium-sized bowl. Add the oregano and cumin to one half of the marinade and stir to combine.
Place half of the chicken cubes into each of the bowls. Stir to coat the chicken well. Cover and marinate in the fridge for one hour.
Meanwhile, soak 6 12-inch wooden skewers in water to cover for at least 30 minutes, to prevent them from burning on the grill.
Skewer the more seasoned chicken, alternating two pieces of chicken with one piece of lemon, using 6 pieces of chicken and 3 pieces of lemon total on each skewer, using 3 of the 6 skewers. Skewer the plainly marinated chicken on the remaining skewers, adding the lemon wedges in the same fashion if desired, or skipping the lemon if you feel like that will be too much citrus for the kids.
Preheat the grill to medium (see Note below). Grill the kebabs for 4 minutes, covered, until browned on the bottom, then turn, and grill, covered, for about 4 minutes more for breasts, 6 more minutes for thighs. Cut into a piece to see if it is cooked thoroughly. Serve with the optional Tzatziki (below), and couscous, rice or orzo, if desired. You can eat the lemons, which caramelize during cooking, or not, as you like.
To make the tzatziki, put the grated cucumber in a colander and sprinkle with a generous teaspoon of coarse or kosher salt. Let sit for 15 minutes, then rinse the cucumber with cold water and squeeze it as dry as possible using your hands.
Put the grated cucumber in a bowl, Add the yogurt and stir to blend. Add the garlic, mint, olive oil, and vinegar and mix well. Cover with plastic wrap and refrigerate until needed.