Lambert joined Liverpool as an amateur at 13 years and 189 days of age in January 1936, becoming the youngest-ever player to join a League club at that time. Although the Welshman had signed amateur forms for Liverpool before World War II he didn't get an opportunity to represent his club in a competitive fixture until 1946. Regional leagues were still operating in the immediate aftermath of the war but, Lambert did play in four FA Cup ties for the club that year, by which time he was 23 years old. Lambert was a reliable full-back who became an integral member of the team for the next decade, averaging over 30 Football League matches per season during that period. He could play on either flank and was a fans' favourite.

Lambert's early years at Anfield were a lot more successful than those near the end of his playing career. He was able to celebrate the first post-war League championship in 1947 and also helped his club reach their first Wembley cup final in 1950. After that, although his own form was as steady as ever, the club's final league placing gradually worsened until relegation to the Second Division was confirmed at the end of the 1953/54 season. Lambert, who was also capped five times by his country in full internationals to add to the caps he had already won as a schoolboy international, remained on Liverpool's books for a further two seasons before retiring a few weeks short of his 34th birthday. He was offered a move to third division north's Chester in December 1955, but didn't want to leave the club for which he had already played his last first-team game.