Set the oven to 425°F and line a sheet pan with foil or parchment.
Whisk together 1 ½ teaspoons salt with the turmeric, cumin, cayenne, and 1 tablespoon plus 2 teaspoons oil in a medium bowl. Add the chicken and stir to coat. Transfer to the sheet pan in a single layer. Add the onions to the bowl with the remaining olive oil and another sprinkle of salt. Stir to combine and arrange the onions around the chicken. Place in the oven.
Roast the chicken until the meat is browned, with an internal temperature of 160°F and the onions are cooked through and caramelized at the edges, 25 to 30 minutes.
While the chicken is cooking, rinse the rice in a strainer until the water runs clear. Add it to a medium saucepan with 4 cups of water and a pinch of salt. Bring to a boil, turn the heat down to low, and cover the pot. Cook for about 10 minutes, then let it rest, covered, until ready to serve.
Place the yogurt in a small bowl and use a microplane to grate in the garlic. Stir in remaining ½ teaspoon salt and half of the lemon juice. Add optional black pepper, stir to combine, and taste and adjust seasoning.
Arrange rice on a platter, followed by the onions and chicken thighs. Scatter cucumber slices and cilantro over the top of the chicken, then finish with remaining lemon juice and another pinch of salt. Serve with rice and yogurt sauce.