French Meaning: The name Lyra is a French baby name. In French the meaning of the name Lyra is: Of the Iyre. Song. Greek Meaning: The name Lyra is a Greek baby name.In Greek the meaning of the name Lyra is: Lyre (medeival instrument). Lyrical.n French the meaning of the name Lyra is: Of the Iyre. Song. Greek Meaning: The name Lyra is a Greek baby name. In Greek the meaning of the name Lyra is: Lyre (medeival instrument).