Lukko's Liiga rivals Ilves and KalPa both exited the competition earlier this evening at the hands of Swedish opposition, but a 3-1 win at home in the first leg gave the Rauma side hope of avoiding a similar fate.
An early goal would have really put them in control of the tie, but the first 20 minutes passed without incident, though Lukko had twice the number of shots on goal as their Swiss hosts.
And the Finnish side were punished for not capitalising when on top, as Gregory Hofmann broke the deadlock on the night for Zug in the second minute of the second period, and 10 minutes later Tomas Tatar struck to level the tie on aggregate.
The two sides were preparing for a winner-takes-all final period, but an interference call against Lukko's Nuutti Viitasalo in the final minute of the second gave Zug a huge chance to go ahead - which they took - Hofmann scored again with just six seconds remaining to put the hosts 4-3 in front.
A tripping call sending Andreas Wingerli to the penalty box five minutes into period three, but as in the first period, Lukko could neither take advantage nor find the net despite dominating the shot count.
Home goaltender Leonardo Genoni made 11 saves in the final period and 30 in total, as his shutout allowed Zug to celebrate the 3-0 win on the night, 4-3 on aggregate.
Despite all three Finnish sides finishing in the top five of the CHL Regular Season, none of them have made it to the Semi-finals, while Sweden's Frolunda are the only team from the Regular Season's top eight to reach the last four.