Lourdes Lopez, a Balanchine-trained dancer, will have big toe shoes to fill when she succeeds Miami City Ballet artistic director Edward Villella next year.

Dubbed a “charismatic former ballerina” by the New York Times, Ms. Lopez co-founded Morphoses Dance Company in New York with renown choreographer Christopher Wheeldon in 2007. When Mr. Wheeldon departed as Morphoses’ artistic director in 2010, Ms. Lopez proved her critics wrong by reinventing the dance company with a rotation of resident artistic directors for the contemporary ballet troupe.

She didn’t fold. The show went on...