Bring stock to a simmer in a medium saucepan.
Heat 2 tablespoons oil over medium heat in another saucepan. Cook onion, stirring frequently, until soft, 6 to 7 minutes. Add rice, cook, stirring, until edges are translucent, 2 to 3 minutes. Add wine; cook, stirring, just until evaporated.
Add 1/2 cup hot stock; cook, stirring, until almost absorbed. Continue adding 1/2 cup stock in this manner until liquid is creamy and rice is al dente, about 20 minutes total (you may not need to add all the stock). Add asparagus with the last addition of stock, and the peas about 1 minute before risotto is done.
Remove from heat; stir in lemon zest and juice, parsley, cheese, and remaining 2 tablespoons oil. Season with salt and pepper. Serve immediately with additional cheese and lemon zest.
To make this dish even healthier, replace the Arborio rice with fiber-rich pearl barley or a whole grain such as farro.