Pat thighs dry; add 1/2 teaspoon salt and pepper. Heat oil in 12-inch skillet over medium-high.
Cook unfolded thighs 6 to 7 minutes on first side, 5 to 7 on second, until browned and thickest part at least 165°F. Plate.
Reduce to medium. Add asparagus and remaining salt; cook 4 minutes, turning, until bright green and lightly browned.
Add butter and garlic; stir 1 minute. Add broth; cover and cook 2 minutes until asparagus tender. Add lemon juice.
Return chicken and juices; turn in garlic butter 1 minute. Serve thighs with asparagus and pan sauce.