After attending college in West Virginia, Lambert attended the
University of Michigan Law School. He was president of the law school class of 1919. Lambert was often referred to by the nickname "Paddy" while attending Michigan. With Lambert's enrollment at Michigan, the press anticipated that he would play for
Fielding H. Yost's
Michigan Wolverines football team. The
Boston Evening Transcript wrote about the prospects for Michigan's 1915 football team: "It will be necessary to develop a new centre, and for this post there is Lambert, a new-comer to Ann Arbor from Wesleyan University of West Virginia, where he made an enviable reputation." Although he played for Michigan's All-Freshman team in 1915, Another press report noted that Lambert, who had played on the All-Freshman team in 1915, was a surprise addition to the team in mid-October: "Lambert played at West Virginia several years ago and was a member of the All-Fresh in 1915. He did not play on the varsity this fall and has been in a uniform only a little over a week. He is light, but an accurate passer and a fighter." Lambert was reportedly the lightest man on the
1917 Michigan Wolverines football team at 160 pounds. Yost did not play Lambert until the season's fourth game against the
University of Detroit on October 17, 1917. Lambert had a strong showing in his first game for Michigan. The University of Michigan yearbook reported on his performance against Detroit: "The West Virginian managed to make about 50 percent of the tackles and would have made more but for the fact that the rest of the players got jealous and started to work." The same publication noted that Michigan's game with
Cornell (a 42–0 win) found "
Weston [Michigan's quarterback) and Lambert feeling like the historical million dollars." The
Detroit Free Press credited Lambert with "opening inviting holes" for Michigan's backs in the Cornell game. Prior to the final game of the 1917 season against
Northwestern, Lambert,
Archie Weston and two other Michigan players were declared ineligible. In Lambert's case, the ruling was due to a
Western Conference rule limiting players to three years of varsity sport, which Lambert had used while at West Virginia Wesleyan. The
Michiganensian noted: "Several little matters, like Conference rules and studies, kept several Michiganders out of the Northwestern fray ... It was decided that Lambert had played enough football, although he was ranking high in his studies." On losing to Northwestern without Lambert in the lineup, Coach Yost complained that "the defense was in the law library." Eckersall also placed Lambert on his All-Western team. While attending Michigan, Lambert was also a member of the Griffins, the Archons, the Barristers,
Sigma Chi,
Phi Delta Phi, and
Michigamua. He was also chosen to serve as a student member of the university's Board in Control of Athletics for the year 1918–19. ==Later years==