Meaning of Lene. Dutch name. In Dutch, the name Lene means-the light of the sun.The name Lene originated as an Dutch name. The name Lene is most often used as a girl name or female name.Dutch Name Meaning-the light of the sun. Origin-Netherlands.eaning of Lene. Dutch name. In Dutch, the name Lene means-the light of the sun.The name Lene originated as an Dutch name. The name Lene is most often used as a girl name or female name. Dutch Name Meaning-the light of the sun.