Since the 2010 release of her debut album Lights, Ellie Goulding has become known for her versatile catalog of pulsing dance music, radio-friendly synth-pop and “folktronica.” But on Nov. 20, the U.K.

More than a year after Britain’s next big thing dropped her electro-pop single “Lights” in the U.S., it’s finally reached Billboard’s top tier—just in time for Goulding, 25, to put the finishing ...