Cut slits into lamb shank in a criss-cross pattern about 1 inch apart and 1/2 inch deep; place into a shallow dish.
Whisk olive oil, rosemary, thyme, basil, parsley, mint, black pepper, salt, and cayenne pepper together in a bowl; brush evenly over the lamb shank. Refrigerate lamb at least 1 hour.
Preheat grill for medium heat and lightly oil the grate.
Stir lemon juice and honey together in a small bowl until smooth.
Cook lamb shank on preheated grill, basting every 15 minutes with the lemon juice mixture, until browned on the outside and red in the center, about 30 minutes per side. An instant-read thermometer inserted into the center should read 125 degrees F (52 degrees C).
Add a half hour more cooking time for each degree of doneness you desire (i.e. another half hour for medium rare, an additional hour for medium, etc.)