Lugo is a Spanish surname named after the city of Lugo in Galicia, Spain. Also Hispanio Celto & Gaulish in original ancient Latin. Short for Lugotorix which means Light or Another name for Lughus
These are patrilineal descendants of the original House of Lugo, a noble family in Lugo.
The shortened form Lugo is likely a branch of the original de Lugo lineage, as in similar cases (e.g. Peña and de la Peña).