Season the chicken thighs with salt and the lemon pepper.
Add the oil to a large cast-iron skillet or sauté pan set over medium-high heat. Once the oil is hot, arrange half of the chicken thighs skin side down and cook them undisturbed until they are golden brown and release naturally from the pan, about 6 minutes. Flip the chicken thighs once and continue cooking an additional 2 minutes.
Transfer the chicken thighs to a plate, then repeat the browning process with the second half of the chicken thighs, transferring them to the plate once fully cooked. Leave all drippings in the pan.
Increase the heat to medium-high. Add the lemon juice to the skillet and cook, scraping up any brown bits with a wooden spatula, until it has reduced by half, about 2 minutes.
Reduce the heat to medium-low then add the butter and cook just until melted. Whisk in the flour and cook, stirring, for 1 minute. (The mixture will be very thick.)
Whisk in the chicken broth and heavy cream.
Return the chicken thighs and any juices to the skillet, arranging them in a single layer, and cook until the chicken thighs reach an internal temperature of 165°F, 10 to 15 minutes.
Transfer the chicken thighs to serving plates and spoon the sauce on top. Serve immediately.