Slice each chicken breast in half lengthwise to make 4 thin cutlets; season both sides with garlic powder and lemon pepper, and add salt if the lemon pepper is unsalted.
Heat the olive oil and butter in a large skillet over medium-high heat until hot and the butter is melted.
Sear the chicken cutlets 5–6 minutes per side, or until golden and cooked through; transfer to a plate and tent with foil to keep warm.
Reduce heat to medium and add the minced garlic to the skillet; cook about 30 seconds until fragrant.
Pour in the chicken broth and lemon juice, scraping up any browned bits from the pan.
Add the cream and the uncooked gnocchi, stirring to submerge the gnocchi in the liquid.
Simmer gently, uncovered, for 5–7 minutes, stirring occasionally, until the gnocchi is cooked through and the sauce has thickened; add a splash of broth if the sauce becomes too thick.
Remove the pan from heat, stir in the grated Parmesan and the baby spinach until the spinach wilts and the sauce is combined.
Return the chicken to the skillet with any accumulated juices, spoon sauce over the top, season with salt and pepper if needed, and serve immediately.