Grate lemon rinds to equal 2 teaspoons; halve lemons crosswise and reserve. Combine rind, oregano, canola oil, and garlic in a large bowl. Add chicken; toss to coat.
Heat a grill pan over medium-high. Coat pan with cooking spray. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add chicken to pan; cook 5 minutes on each side or until done. Add lemon halves to pan, cut sides down; cook 4 minutes. Remove chicken and lemons from pan. Cut chicken into slices.
Coat asparagus and green onions with cooking spray; add to pan. Cook 3 to 4 minutes or until charred and tender, tuning occasionally. Cut asparagus and green onions into 2-inch pieces.
Combine remaining 1/2 teaspoon salt, remaining 1/4 teaspoon pepper, olive oil, and vinegar in a large bowl. Add asparagus, green onions, and arugula; toss. Serve with chicken and lemon halves.
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