Heat grill to high. Place lemon juice and sugar in a medium saucepan and bring to a boil on the grates of the grill. Cook until reduced to 1/2 cup. Remove from heat and let cool slightly.
Place cooled lemon syrup, vinegar, salt, and mustard in a blender and blend until combined. With the motor running, slowly add the olive oil until emulsified. Stir in the pepper.
Brush sardines with oil and season with salt and pepper on both sides. Grill for 3 to 4 minutes per side or until just cooked through.
Brush bread on both sides with olive oil and season with salt and pepper, to taste. Grill for about 45 seconds per side. Place each slice of bread on a plate and top with a sardine. Drizzle with vinaigrette and garnish with chopped parsley.