Slice chicken breasts into 8 thinner cutlets lengthwise. Pound with a rolling pin or flat side of a meat mallet into same thickness pieces. Season with salt and black pepper on both sides. Set aside.
Preheat large skillet on medium heat and swirl 1 tablespoon of olive oil to coat. Pan fry chicken until golden brown or for about 6 minutes per side. Transfer onto a plate and set aside.
Return skillet to medium heat and add remaining 1 tablespoon of olive oil. Add onion and cook until softened, stirring occasionally. Add garlic and saute for another 30 seconds, stirring a few more times.
Add flour and stir until combined. Now start adding chicken broth in small increments while stirring, until thick roux forms. Then add milk, heavy cream, remaining salt, pepper, stir and bring to a boil. Add lemon juice and give sauce quick mix.
Add previously cooked chicken, making sure to cover it in sauce, and simmer on low heat for 5 minutes or until sauce has thickened a bit and chicken is tender. Sauce will thicken more as it stands. Tuck in lemon slices.