Trim the chicken breasts and slice each breast lengthwise into 2–3 strips, then place the strips in the Instant Pot insert in a single layer if possible.
Zest both lemons, then cut them in half and squeeze the juice into a bowl.
Whisk together lemon zest and juice, Greek seasoning, olive oil, chicken stock, Greek oregano, and black pepper until well combined.
Pour the lemon-and-herb mixture over the chicken in the Instant Pot, ensuring the strips are coated.
Seal the Instant Pot and set to Manual/High Pressure for 8 minutes, then allow a 10-minute natural pressure release before carefully releasing any remaining pressure.
Remove the cooked chicken with a slotted spoon to a cutting board, leaving the cooking liquid in the pot.
If the sauce seems very thin, use the Sauté function on high for a few minutes to reduce it slightly.
Shred the chicken with two forks, return the shredded chicken to the Instant Pot, and stir gently to coat with the sauce; keep warm on the low setting.
To make the Greek salsa, chop cucumbers, tomatoes, Kalamata or black olives, and red onion; combine them in a bowl and stir in 1/4 cup Italian dressing, then gently fold in crumbled feta.
Heat tortillas in a dry skillet over high heat until warmed and pliable, about 20–30 seconds per side.
Assemble tacos by filling each warm tortilla with a generous scoop of hot shredded lemon chicken and topping with a spoonful of Greek salsa, then fold and serve.