Remove frozen cauliflower rice from the freezer to thaw at room temperature while you prepare the chicken.
Trim chicken breasts and cut each lengthwise into 2–3 strips; place the strips in the Instant Pot insert.
Zest two lemons, then halve and juice them. In a bowl whisk together lemon zest, lemon juice, 1 tablespoon Greek seasoning, 2 tablespoons olive oil, 1/4 cup chicken stock, 1/2 teaspoon Greek oregano, and 1/2 teaspoon freshly ground black pepper to make the cooking sauce.
Pour the sauce over the chicken in the Instant Pot, secure the lid, set to Manual/High Pressure for 8 minutes, then allow a 10-minute natural release before releasing any remaining pressure.
When pressure is fully released, remove chicken with a slotted spoon to a cutting board and shred with two forks. If the Instant Pot has excess liquid, use Sauté on high for a few minutes to reduce it; then return shredded chicken to the pot and gently stir to coat. Keep warm on the low or warm setting.
Make the Greek salsa: chop cucumbers, tomatoes, Kalamata (or black) olives, and red onion. Toss the chopped vegetables with 1/4 cup Italian dressing, then gently fold in crumbled feta. Set aside.
If using fresh cauliflower, remove leaves and cut into pieces; pulse in a food processor or grate to make cauliflower rice. If using semi-thawed frozen cauliflower rice, proceed to the next step.
Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add chopped green pepper and chopped yellow onion and cook about 3 minutes until softened and beginning to brown.
Add 1 tablespoon Greek seasoning to the skillet and cook 1 minute, then add the cauliflower rice. Cook, stirring occasionally, until heated through and some moisture has evaporated, about 3–4 minutes for semi-thawed cauliflower (fresh may take a few minutes longer). Season with salt and fresh-ground black pepper to taste.
To assemble bowls, divide hot cauliflower rice among serving bowls, top with a generous scoop of shredded lemon chicken, and finish with a scoop of the Greek salsa. Serve immediately.