In a shallow dish, mix the all-purpose flour, lemon pepper seasoning, and salt until evenly combined.
Coat the chicken tenderloins in the seasoned flour mixture, tossing to cover all sides and shaking off excess.
Heat 1 tablespoon of olive oil in a large skillet over medium heat until shimmering.
Place a single layer of coated chicken tenders in the skillet and cook undisturbed 3–5 minutes, until the underside is golden.
Flip the tenders and cook another 3–5 minutes, until cooked through and internal temperature reaches 165°F (74°C). Remove to a plate and keep warm; add more oil if cooking remaining chicken in batches.
Reduce the heat to low. Add the remaining 1 tablespoon olive oil (if any left) and the butter to the skillet, then pour in the fresh lemon juice to deglaze the pan, scraping up any browned bits.
Return the cooked chicken tenders to the skillet and toss gently to coat in the lemon-butter sauce.
Transfer to a serving plate, sprinkle with chopped parsley if desired, and serve immediately.