Place the arugula and in a large serving bowl.
In a medium skillet heat 2 tablespoons of olive oil over medium-high heat. Add the radicchio and salt, sear for 45 seconds to 1 minute. Pour the radicchio over the arugula. Set the skillet aside.
Decrease the heat to low. Off of the stove, add 1 tablespoon of olive oil, garlic and red pepper flakes to the skillet. Place the skillet back on the stovetop and heat for 1 minute, stirring once or twice.
Increase the heat to medium and add the balsamic and lemon juice. Bring to a boil and reduce the heat to low. Simmer for 5 minutes.
Pour the balsamic reduction over the radicchio and arugula. Add the onions, cheese and lemon zest and then toss well to combine. Serve warm topped with parmesan cheese and lemon juice.