Heat the olive oil in a large skillet over medium-high heat.
Season the chicken pieces with salt and pepper, add to the skillet, and cook until the bottoms are golden, about 2–3 minutes.
Flip the chicken and cook an additional 2–3 minutes until cooked through; transfer the chicken to a plate.
Add the butter to the skillet and let it melt, scraping up any browned bits from the bottom.
Add the minced garlic and sauté for about 20 seconds until fragrant.
Pour in the chicken broth and water and stir to combine.
Add the refrigerated tortellini, cover the skillet, and bring to a gentle boil; cook, stirring occasionally, until the tortellini are tender, about 2–4 minutes—do not overcook.
Stir in the pieces of Neufchâtel, the grated Parmesan, and the lemon juice until the cheeses melt and form a creamy sauce.
Return the cooked chicken to the pan, add the baby spinach, and toss until the spinach wilts and everything is well combined; taste and adjust salt and pepper if needed.
Remove from heat, cover, and let rest for a few minutes to allow the sauce to thicken slightly, then serve warm.