1) Preheat the grill to medium-high. Brush the onion and fennel slices with oil; season generously with salt and pepper. Grill over medium-high heat until onion and fennel caramelize and soften, showing grill marks. Reduce the heat and continue cooking onion and fennel until soft. Remove from the heat, let cool, and finely chop.
2) In a bowl, add the grilled onion and fennel, rosemary, lemon zest, lemon, honey, and chili flakes. Season to taste.
3) Gently form the lamb into eight burgers; make sure the meat is not compressed. Season generously with salt and pepper and grill to desired doneness.
4) Remove some of the bread from the rolls to make a better bread-to-burger ratio. Grill the rolls briefly and let cool. Spread both sides of the rolls with mayonnaise, add a spoonful of the onion relish, some arugula leaves, and the lamb burger. Serve immediately.