At the 2012 Summer Olympics, Vila competed for Argentina in the men's tournament. Lucas won the bronze medal at the 2014 Men's Hockey World Cup and three medals at the Pan American Games. He was part of the Argentinian squad which won the gold medal at the 2016 Summer Olympics. In 2018 he was selected for the 2018 World Cup which means he has played in four consecutive World Cups. He scored 1 goal in four matches in that tournament. In July 2019, he was selected in the Argentina squad for the 2019 Pan American Games. They won the gold medal by defeating Canada 5-2 in the final. In December 2019, he was nominated for the FIH Player of the Year Award.