The third-seeded Lambeth and Pitts defeated Alan Dubrovsky and Walker Anderson of Hobart (NY) College 6-1, 6-4 in the consolation playoff for seventh.
In Friday's consolation semifinals, the Trinity duo lost a barn-burner to the #2 team of Tyler Raclin and Jeremy Yuan of the University of Chicago (IL) 3-6, 6-4, 10-8.
Trinity's duo qualified for the ITA Cup by winning the ITA Southwest Doubles Championship last month in Abilene, Texas.
Lambeth competed in his second ITA Cup, formerly known as the National Small College Championships. In 2016, Lambeth paired with current teammate Matt Tyer to win the ITA Southwest Championship, and the duo advanced to the national event.
Trinity's dual-match season begins in February.