Neil Lennon's men currently enjoy a huge 16-point lead over second-placed Motherwell and are on course to clinch their second successive league crown a handful of games early. Their Champions League campaign, meanwhile, could also come to an end on Wednesday after travelling to Turin 3-0 down to Juventus from last month's first leg.
But after being paired against Dundee United for the last four, Lustig hopes interest can be maintained in competitive action right up until the domestic season's climax at Hampden on May 26. The Swede said: "It's a tough draw. Dundee United are a very good team but if you want to win the cup, you have to beat the team in front of you."
He continued: "Winning the cup would mean a lot. Hopefully the final will be our last game of the season and we can make something good out of that. Winning this game could keep our season alive. It's a trophy and we want to win it."
Falkirk teenager Ryan McGeever, meanwhile, has revealed how he never got the chance to run out with former club Queen's Park at Hampden. But now the 18-year-old defender says he is preparing for the biggest game of his life at the National Stadium after the Bairns were paired with Hibernian in the William Hill Scottish Cup semi-finals.
He said: "I came up through the youth system at Queen's Park but I actually never had the chance to play for the first team. So my first game at Hampden will be against Hibs and it will definitely be the biggest game of my career so far.
"It was disappointing never to have made an appearance for Queen's Park's first team but if you were giving me the choice of playing there for them or against Hibs in a Scottish Cup semi-final, I know what one I'd pick."
McGeever was happy to avoid Celtic in the last four but so too was the skipper of their opponents, James McPake.
The Hibs captain said: "It's the best draw we could have hoped for.
"We have avoided the two SPL teams but I don't think Falkirk will be any easier because they are a league below us. They are in the semi-final on merit and are a good team. Their manager Steven Pressley is doing well there and it will be a tough game."