Combine the olive oil, balsamic vinegar, garlic, sugar and salt and pepper in a large bowl, whisk until well combined. Add the mushrooms and stir gently to coat. Cover and set aside for 30 minutes, stirring every now and then to coat the mushrooms.
Meanwhile, preheat barbecue plate on medium-high heat. Lightly spray asparagus and both sides of the lamb. Season with salt and pepper. Barbecue the asparagus for 2-3 minutes or until just tender, transfer to a plate. Barbecue the lamb for 3-4 minutes each side for medium or until cooked to your liking. Transfer to a tray, cover loosely and set aside to rest 5 minutes.
To complete the salsa, cut the asparagus into 1cm-thick slices and add to the mushrooms. Remove the seeds from the tomatoes and dice the flesh. Add to the mushrooms with the pine nuts and mint, stir gently to combine. Serve with lamb.