Luca is the product of Switzerland's GCK Lions junior program where he rose quickly as a leader for their Junior A team. In 2005 he played for Switzerland's U18 World Junior Championship team scoring 1 goal and 2 points in 6 games with a -2 rating which tied for the team lead in scoring as the Swiss finished 9th in the tournament. In 2005-2006 he made his men's league debut in the second tier NLB going scoreless in 7 games with 2 penalty minutes. In 2006-2007 he played 13 games with GCK's Junior A team scoring 9 goals and 16 points in 13 games with 22 penalty minutes. He also played 10 games at the NLB level split between GCK and HC Thurgau in which he totaled 2 goals and 3 points with 8 penalty minutes. At midseason he appeared in 3 games for Switzerland's U20 World Junior Championship team and was scoreless as the Swiss ended the tournament by going 3-0 in the relegation round. After his club team season he appeared in 6 games for Switzerland's U18 World Junior Championship team scoring 3 goals and 4 points with 6 penalty minutes and a -5 rating. The Swiss team finished 6th in the tournament. He was rated the 12th best European skater in his draft class by the NHL Central Scouting Service and the 54th best prospect by Red Line Report. Cunti was drafted by the Chicago Steel of the USHL and was place on their July 1, 25-man protected list for the 2007-2008 season. He was passed over in the CHL Import Draft. The Lightning selected Cunti in the 3rd round, 75th overall, in the 2007 NHL Entry Draft. After a short recruiting period, Cunti committed to play for Saint Cloud State of the NCAA and enrolled at the school for the Fall semester. Unfortunately, the NCAA was extremely slow to make a decision regarding Cunti's elligibility due to the handful of professional games Cunti played in the NLB in Switzerland. At the Fall semester Cunti was compelled to leave school rather than face the possibility of not playing any hockey at all in the 2007-2008 season and he joined the Steel in the USHL. With Chicago, Cunti lived up to his reputation as a scorer by potting 11 goals and 32 points in 34 regular season games in his first taste of North American hockey. Cunti also added 28 penalty minutes and was +16 in the regular season. Cunti's presence helped the Steel lock up the final playoff spot in their division and pull off a stunning first round upset of top seeded Indiana in the playoffs. Cunti finished tied for second on the Steel in playoff scoring with 2 goals and 5 points in 6 games with 2 penalty minutes and a +1 rating. Unfortunately, prior to the playoffs, he received final word from the NCAA that he is inelligible to ever play in the NCAA. Cunti was selected by Rimouski Oceanic in the 2008 CHL draft and will play at least a year in juniors.
Cunti was selected by Rimouski Oceanic in the 2008 CHL draft, so his pro career is on hold for at least another season.
