When the only hospital in a small central Wyoming city stopped delivering babies and cut back on surgeries, local residents sought to start their own. LifePoint Health Inc., backed by Apollo Global Management Inc., green up pointing triangle controls the only hospital in working-class Riverton, Wyo. After LifePoint merged Riverton’s hospital with another facility it owns in the city of Lander, 30 miles away, it began consolidating the hospitals’ services.