Preheat the oven to 375 degrees.
In a Dutch oven, heat the oil and saute the rabbit in batches over medium-high heat, turning occasionally, until golden brown on all sides. Lightly salt the rabbit (feta is usually quite salty), sprinkle with plenty of pepper and return the rabbit to the casserole. Add the garlic and cook, stirring, for 2 minutes; do not let the garlic color.
Pour in the wine, sprinkle with the dried oregano and stir in the cheese. Add enough stock to come two-thirds of the way up the sides of the rabbit. Bring to a boil, cover, and transfer the casserole to the oven. Bake, covered, for about 1 hour.
Turn the rabbit pieces, add 3 tablespoons lemon juice and bake for 30 minutes more, or until the meat is very tender. Transfer the rabbit to a heated plate and cover with aluminum foil to keep warm.
Reduce the sauce on top of the stove over high heat until thickened; taste and adjust the seasonings, adding more lemon juice if necessary; the sauce should be quite lemony. Whisk in the butter and pour the sauce over the rabbit. Sprinkle with the chopped oregano, if desired, and serve at once.