In a small bowl, combine salt, pepper, smoked paprika, and herbs de Provence.
Trim any fat from chicken breasts, then season with the spice mixture; both sides.
Add 1 Tbsp. of the olive oil to the cooking pot and set to sauté. When the oil is hot, add 2 of the seasoned chicken breasts. Sauté about 3 minutes until golden brown. Turn and cook the other side, about 2 minutes. Remove the chicken to a plate. Add the second tablespoon of olive oil and the remaining two chicken breasts and sauté until golden brown on each side. Remove the chicken to the plate with the first two chicken breasts. Turn the Instant Pot off.
Pour the chicken stock into the cooking pot. Using a wooden spoon, scrape up any brown bits from the bottom of the pot. Place the Instant Pot trivet into the cooking pot and place the 4 chicken breasts on the trivet.
Put the lid on the Instant Pot and lock into place. Make sure it is set to the "SEAL" position. Select the high pressure cooking function with timer set at 4 minutes. When cycle finishes, let pressure release naturally for 4 minutes. After 4 minutes, finish releasing pressure using the manual release method. Remove Instant Pot lid carefully. Remove chicken and place on a plate. Remove trivet from cooking pot.
Set the Instant Pot to the "Sauté" function. In a small bowl, whisk together 3-4 Tbsp. of water and 2 Tbsp. of cornstarch; use enough water to make a slurry. Add the cornstarch slurry to the cooking pot and bring the mixture to a boil, whisking frequently. Let the sauce simmer for 2-3 minutes until thickened.
Turn off Instant Pot and stir in the lemon juice. Season to taste. Spoon pan sauce over chicken breasts and serve.