Hailing from Austevoll, Norway, he joined Brann as a junior player with his senior debut coming in 1993. Lundekvam eventually gained a regular place as a central defender before being sold to English side Southampton in the autumn of 1996. He was the team's first choice for captain for several years. Lundekvam made his debut for Norway in November 1995, but did not become a regular until 2002. He was capped 40 times, scoring twice. His first international goal, against Bosnia-Herzegovina in 2002, was the 1,000th goal in the history of the Norwegian national team. He scored only two goals during his Saints career. His first came against Wolverhampton Wanderers on 3 April 2004 in a 4–1 win, and his second against Cardiff in 2006 – both teams managed at the time by former Saints manager Dave Jones. In 2002–03, he contributed to what was undoubtedly Southampton's best season since the 1980s, when they finished eighth in the Premier League and reached the FA Cup final, where they only narrowly missed out on silverware as they lost 1–0 to Arsenal. This was during the management of Gordon Strachan, who famously joked when Lundekvam was stretched off injured in a game against Leicester City in the 2003–04 season that he "didn't have a clue" whether the player was unconscious as "that's what he's always like". Lundekvam remained at Southampton after their relegation from the FA Premier League in 2005. He went off injured after five minutes of the first game of the 2006–07 season, away to Derby County on 6 August 2006 and missed the first two months of the season. He then enjoyed a long run in the team before another injury in March put him out for another month. In the game at St Mary's against Southend United on 6 May 2007, he fell awkwardly sustaining a serious ankle injury which put him out of action. On 18 March 2008 it was announced that his injury was such that his playing career was over.
Later career
He later had problems with drink and drug abuse. He quoted "I would drink two litres of hard liquor and do between five and ten grams of cocaine every day." In July 2012, Lundekvam claimed that he, team-mates and opposing captains were involved in betting fraud. "We could make deals with the opposing captain about, for example, betting on the first throw, the first corner, who started with the ball, a yellow card or a penalty. Those were the sorts of thing we had influence over." These allegations were later denied by Lundekvam's former team-mate and captain, Francis Benali. Following his retirement, Lundekvam returned to Norway with his wife Nina, their two children and a dog named Lucky. Lundekvam works regularly as a pundit for TV2, the largest commercial broadcaster in Norway.
