Lambert attended Wayne County High School in Jesup, Georgia, where he was teammates with Tre' Jackson. In his three varsity seasons, he had 4,282 passing yards and 38 touchdowns. He was rated by Scout.com as a four-star recruit and was ranked among the top quarterbacks in his class. He committed to the University of Virginia to play college football.
College career
Lambert redshirted his first year at Virginia in 2012. As redshirt freshman in 2013, he appeared in seven games, passing for 340 yards with one touchdown and two interceptions. Lambert took over as Virginia's starting quarterback in 2014. Overall, he started nine games, completing 154 of 261 passes for 1,632 yards with 10 touchdowns and 11 interceptions. In June 2015, Lambert transferred to the University of Georgia. In his first year at Georgia he was named the starter. During the third game of the season, he completed 24 of 25 passes for a 96% completion percentage, which set an NCAA record. He also broke Georgia's record for consecutive completions with 20. Lambert had an inconsistent career at the University of Georgia. After he transferred from the University of Virginia at the beginning of the 2015 year, Lambert was named the starting quarterback for the Georgia Bulldogs. Perhaps his most memorable moment that year came against the University of South Carolina. Going into that game, the Bulldogs were 2–0 on the season, but questions about Lambert as the starting quarterback still remained. In the previous game against the Vanderbilt Commodores, Lambert had gone 11–21 for 116 yards with no touchdowns or interceptions. Most of his pass attempts had barely crossed the line of scrimmage, and many had questioned if he truly had the arm talent to be the University of Georgia’s starting quarterback over several talented underclassmen including Brice Ramsey and Parker McLeod. There were some rumors that if Greyson Lambert did not play well against South Carolina, he would lose his starting position. Lambert laid to rest any doubts or questions about his ability to play the quarterback position against the South Carolina Gamecocks. Lambert went 24–25 for 330 yards, 3 touchdowns, and no interceptions. After missing one pass in the back of the end zone late in the first quarter, he went on to complete his final 20 passes of the game, setting a school record. "I can't believe he threw an incompletion," head coach Mark Richt quipped. "I'm disappointed in that. But we'll forgive him." The previous best was 19 straight completions by former Georgia quarterback Mike Bobo in the 1998 Outback Bowl. The rest of the season would prove to be much more of a tough grind than the South Carolina game. Georgia ended up with 3 losses by the end of the year, and they were fairly lucky to not end up with more. They won in overtime against in-state rival Georgia Southern. They also had close 1 possession victories against several below.500 teams such as Georgia Tech, Auburn, and Missouri. Lambert never came close to the production output he showed against South Carolina, finishing the season averaging only 167.6 passing yards per game. Lambert and the Bulldogs finished the season with a victory over Penn State in the Tax Slayer Bowl. With a record of 10–3, they still were unranked in the final AP Poll. The offseason didn’t go exceptionally well for Lambert either. Georgia’s head coach Mark Richt ended up getting fired due to the disappointing result of the season, and Lambert’s credentials as starting quarterback were questioned even further. Lambert would be a senior in the upcoming season, but his starting spot was not guaranteed. There was a new head coach, Kirby Smart, and a new incoming 5-star quarterback recruit, Jacob Eason. Lambert would be in an open quarterback competition battling against Eason and fellow returning quarterback Brice Ramsey. New head coach Kirby Smart did not announce who Georgia’s 2016 opening day starting quarterback would be until game day. After the opening kickoff, Greyson Lambert trotted onto the field with the rest of the offensive starters to compete against the North Carolina Tar Heels in an AP ranked matchup. Coach Kirby Smart had decided to implement a system where both Lambert and Jacob Eason would put in work at the quarterback position. Eason ended up throwing for more yardage than Lambert, but Lambert was the quarterback for the game-clinching final drive. Georgia won the game 33–24. Jacob Eason went on to start the next game against Nicholls State. He played the whole game until the 4th quarter, where Lambert was brought in to replace him on the final drive. Lambert’s drive bled out the clock to get Georgia to hold on for the closer than expected victory, 26–24. For the rest of the season however, Eason went on to become the #1 quarterback. As of December 6, 2016 before the Autozone Liberty Bowl against TCU, Greyson Lambert’s 2016 stats are 7–12 passing for 56 yards. He had no touchdowns or interceptions. In 2015 Greyson Lambert was the recipient of the Davis Family Football Foundation Scholarship. In 2016 Lambert was the recipient of the Jack and Joy Davis Football Scholarship.
Professional career
Lambert signed with the Texas Rangers Organization as a pitcher in 2017.