Trim the chicken and cut each breast lengthwise into 2–3 strips depending on size.
Grate the lemon zest and squeeze the juice from both lemons. Whisk together the zest, lemon juice, 1 tablespoon Greek seasoning, 2 tablespoons olive oil, 1/2 teaspoon dried Greek oregano, and 1/2 teaspoon fresh-ground black pepper to make the cooking sauce.
Spray the slow cooker insert with oil or nonstick spray. Place the chicken strips in the bottom and pour the cooking sauce evenly over the chicken.
Cook on high for about 3 hours, or on low for about 5 hours, until the chicken shreds easily with a fork.
Use a slotted spoon to transfer the cooked chicken to a cutting board, leaving the sauce in the slow cooker. Shred the chicken with two forks, return it to the slow cooker, and stir to coat with the sauce; keep warm on low while you finish the bowls.
If using frozen cauliflower rice, remove from the freezer to thaw on the counter; if using fresh, cut a large head into florets and process or grate into rice-sized pieces.
Finely chop the green pepper and onion. Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the chopped pepper and onion and cook about 3 minutes until softened and beginning to brown.
Stir in 1 tablespoon Greek seasoning and cook 1 minute, then add the cauliflower rice and cook, stirring or turning occasionally, until it softens and starts to brown, about 3–4 minutes for slightly crisp rice or longer if you prefer softer texture. Season with salt and fresh-ground black pepper to taste.
Chop the cucumbers, tomatoes, olives, and red onion. Combine them in a bowl, stir in 1/4 cup Italian dressing, then gently fold in the crumbled feta to make the Greek salsa.
Assemble bowls by placing hot cauliflower rice in the bottom, topping with a generous scoop of shredded lemon chicken, and finishing with a scoop of the Greek salsa.