McKelvy is mostly a self-taught potter, having developed an innovative new style of pottery. From her Navajo heritage are the distinctive and traditional cooking pot shape and the Yei or deity figures. Lucy gathers her clays, minerals, and pigments near Low Mountain, Arizona. She says about her pottery: "My artwork is influenced by the ceremonies and traditional teachings of my grandfather and of my great-grandmother who partially raised me. Also the pottery from the ancient ruins near my home and my many Pueblo friends who inspired me, and quite possibly some of my Hopi-Tewa ancestry."
It is Lucy's belief that pottery must, to some extent, go beyond traditions. When Navajos tell her that it is wrong to paint Yei figures on her pots— because they are religious figures— she explains that her pottery is a very personal thing, and the decision about which designs to use must be hers also.