Meaning of Lynessa. Welsh name. In Welsh, the name Lynessa means-Variant of ancient Welsh given name Eluned: From cilun meaning idol.. Other origins for the name Lynessa include-Welsh, English, English, English.The name Lynessa is most often used as a girl name or female name.Welsh Name Meaning-Variant of ancient Welsh given name Eluned: From cilun meaning idol.Origin-Welsh.ther origins for the name Lynessa include-Welsh, English, English, English.The name Lynessa is most often used as a girl name or female name. Welsh Name Meaning-Variant of ancient Welsh given name Eluned: From cilun meaning idol. Origin-Welsh.