Answer
Lucius was unable to gain a political office in Tarquinii due to his father's ethnicity. His father, Lucius Tarquinius Priscus, was a Sabine, and the Tarquinii were an Etruscan people. The Etruscans were a dominant force in Italy at the time, and they looked down on the Sabines as inferior. This prejudice made it difficult for Lucius to gain political power in Tarquinii.