2009-10: Lindholm played for the Jonstorps U20 and U18 teams in Swedish Division 1 near his hometown of Helsingborg in southwest Sweden. In three U20 games he scored 1 goal with 2 assists. Lindholm skated in 15 games for the U18 team and scored 3 goals with 4 assists.
2010-11: Lindholm moved up to the SuperElit (U20) division with Rogle BK. In 39 games during the regular season he had 4 assists and was plus-four with 34 penalty minutes. He played in three playoff games and was minus-one with no points or penalties. In 14 games with Rogle BK U18 (including three playoff games) he scored 2 goals with 5 assists and had 12 penalty minutes.
2011-12: Lindholm made his pro debut – skating in 20 games for Rogle BK in AllSvenskan (Sweden's second league) – and played in all 10 qualifying series games. He played for Sweden's silver medal team at the 2012 U18 World Junior Championship and skated for Rogel BK's U20 squad. Lindholm scored 1 goal with 3 assists and was minus-one with 12 penalty minutes during the AllSvenskan regular season. In the ten-game qualifying series he scored 1 goal with 4 assists and was plus-five with 6 penalty minutes. Rogle BK finished second in the six-team tournament to gain elevation to the Swedish Elite League in 2012-13. At the U18 WJC he had 4 assists and was minus-one with 4 penalty minutes. Lindholm scored 5 goals with 12 assists in 28 games for Rogle BK U20 and was named the U20 Super Elit league's Best Defenseman. Lindholm was ranked fourth amongst European skaters in Central Scouting's final rankings prior to the 2012 NHL Draft.