Combine the lamb with the mustard and some salt and pepper and mix to combine. Form into 10 patties and refrigerate for 30 minutes.
Place 1 tbsp of olive oil into a frying pan over a moderate heat and add the sliced onion. Cook for 15-20 minutes or until nicely coloured and crispy, stirring every now and then.
Preheat a char grill or barbecue to moderately high. Brush the patties with the remaining oil and cook for 2 ½ minutes. Turnover, place a cheese slice on top of each patty and cook for a further 2 ½ minutes or until cooked through. Set aside.
Top the bottoms of the buns with the lettuce and tomato, then place a patty on top. Add the onions and a squirt of sauce. Place the lids on top and serve.