To candy walnuts, line cookie sheet with parchment paper; set aside. In medium skillet, simmer sugar, cayenne pepper and water over medium-high heat until it turns golden brown, about 15-20 minutes. Stir walnuts into caramel using wooden spoon. Spoon nuts onto parchment paper and season with salt. Cool then pull nuts apart into smaller pieces.
Prepare dressing by placing walnuts in bowl of small food processor and pulsing. Add lemon juice, walnut oil, olive oil, a pinch of salt and some black pepper. Pulse to blend. Taste for seasoning and adjust as needed.
To assemble salad, toss dressing with grapes and lettuces. Top with candied walnuts and cheese.