Lowry made his debut for the Glory on 30 January 2016, starting against Melbourne Victory. Lowry then scored his first Perth Glory goal on 20 February 2016 when he scored a header in the 41st minutes, to give Brisbane Roar a thrashing with a 6–3 win for Perth Glory. Throughout the 2015–16 season, Lowry established himself in the starting eleven and formed a central defense partnership with Alex Grant, as he made ten appearance for Perth Glory in his first half of the season.
In June 2015, he became the first SMU Mustang to win the NCAA individual championship, recording a score of 280 (−8) to win by one stroke. In August, he won the U.S. Amateur title, defeating Derek Bard 7 & 6 in the 36-hole final. He became the fifth player to win both the NCAA and U.S. Amateur titles in the same year, joining Jack Nicklaus (1961), Phil Mickelson (1990), Tiger Woods (1996), and Ryan Moore (2004).
Hyundai Tournament of Champions: Finished T6 in a Monday-start-Tuesday-finish event, the season-opening, 54-hole Hyundai Tournament of Champions. The event "started" twice during the regularly scheduled first round Friday and later Sunday, but both times PGA TOUR rules staff halted play due to unplayable windy conditions and subsequently voided all scores that had taken place. As the first player off the tee, he ended up hitting three "opening" shots of the season.