In a medium saucepan over medium-high heat, whisk together the sugar, miso, sake and mirin. Bring the marinade to a boil, then remove from the heat, transfer to shallow dish and let cool completely. Add the fish, covering it with the marinade, and refrigerate at least 30 minutes or up to 2 days.
In a small saucepan, bring a few cups of water to a boil. Boil the garlic for 2 minutes and drain on paper towel. In a large skillet over medium heat, cook the blanched garlic in the butter until golden, 2 minutes. Add the mushrooms and cook until golden, about 10 minutes. Add the lemon juice and soy sauce and season to taste with salt and pepper. Keep warm.
Cover a grill liberally with the nonstick cooking spray and heat medium-high. Grill the fish, turning once, until cooked through, about 3 minutes per side. Serve with the buttered mushrooms and rice.
What's the Difference Between Red Miso and White Miso?