Prep the Coating: In a shallow bowl, gently whisk the egg white until it's slightly frothy. In another shallow bowl, mix together the almond flour, grated Parmesan, garlic powder, salt, and pepper.
Coat the Chicken: Pat the chicken tenders completely dry. Dip each tender first into the whisked egg white, then dredge it thoroughly in the flour mixture, ensuring an even coat. Place the coated chicken on a plate lined with waxed paper.
Cook the Chicken: Heat 1 1/2 tablespoons of olive oil and 1/2 tablespoon of butter in a large skillet over medium heat until hot. Add half of the coated chicken tenders and cook for about 3 minutes per side until they're beautifully golden brown. Transfer the cooked chicken to a clean plate. If needed, quickly wipe out the pan to prevent any leftover flour from burning. Repeat with the remaining 1 1/2 tablespoons of olive oil, 1/2 tablespoon of butter, and the rest of the chicken.
Simmer the Broth: In the same skillet, add the minced shallot and garlic and cook for about 30 seconds until they smell fragrant. Pour in the chicken broth and add the lemon slices. Bring the mixture to a gentle simmer and let it cook for about 7 minutes, or until the liquid has reduced by half and thickened a bit.
Finish the Sauce: Stir in the fresh lemon juice and drained capers. Then, add the remaining 3 tablespoons of butter, one piece at a time, stirring constantly until it's fully melted and creates a smooth, luscious sauce. If you want an even thicker sauce, you can whisk in a tiny pinch (about 1/4 teaspoon) of glucomannan or xanthan gum. Taste and adjust seasoning with extra salt and pepper if needed.
Serve: Arrange the golden chicken tenders on plates, perhaps over a bed of lightly steamed zucchini noodles or cauliflower rice for a healthy side. Generously spoon the delicious lemon-butter caper sauce over the chicken before serving.