Rinse the beef liver slices under cold water and pat them dry with paper towels.
In a bowl, combine 2 tablespoons of olive oil, minced garlic, thyme, rosemary, salt, pepper, and lemon juice. Mix well to create a marinade.
Add the beef liver slices to the marinade, ensuring they are well coated. Cover and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
Preheat your grill to medium-high heat. Brush the grill grates with the remaining 2 tablespoons of olive oil to prevent sticking.
Remove the liver from the marinade and let any excess marinade drip off. Discard the marinade.
Place the liver slices on the grill and cook for about 3-4 minutes on each side, or until they are browned and cooked to your desired doneness. Avoid overcooking to keep the liver tender.
Remove the liver from the grill and let it rest for a few minutes before serving.
Garnish with fresh parsley and serve warm.