In a medium saucepan, combine sugar and 1/2 cup water. Place over high heat and whisk until sugar is dissolved. Add lemon juice and whisk to combine. Add walnuts and gently stir, using a heatproof spatula, until coated with sugar mixture. Cover, reduce heat to medium-high, and cook for 5 minutes, stirring twice. Uncover and continue to cook, stirring gently, until caramelized, 2 to 3 minutes more.
Using a fork, quickly remove walnuts individually, and transfer to a baking sheet lined with a nonstick baking mat. Let cool.