Season the chop with salt and pepper. Heat 1/2 tablespoon of the EVOO in a medium skillet over medium-high heat. Cook the chop until golden, 3 to 4 minutes per side, tenting loosely with foil once you turn the chop. Remove the cooked chop to a plate and cover to keep warm. Add the remaining EVOO and the onions and apples. Season with salt, pepper, and the thyme and cook until just tender, 5 to 6 minutes, stirring occasionally. Douse with juice of the 1/2 lemon and remove to the plate with the chop.
Add 1 tablespoon of the butter to the skillet and when it melts, whisk in the flour. Cook for 1 minute, stirring, then whisk in the cider and stock. Season the gravy with salt and pepper. Cook over medium-low heat for 3 to 4 minutes to thicken.
Serve the chop covered with apples and onions, the gravy poured down over the top, and the muffin alongside.