Lakic treble helps Kaiserslautern crush Koblenz
Nuremberg joined them in the last eight with a 2-0 win over third division Kickers Offenbach and will next play Schalke 04.
Both games had been postponed in December because of bad weather.
Nuremberg dominated from the start and took a deserved lead when Timmy Simons pounced on a loose ball in the box to slot home after 20 minutes. He added another just past the hour when the ball deflected off his back into the net.
Kaiserslautern fell a goal behind after 17 minutes and squandered a chance to level when Croatian Lakic, who has netted 11 league goals this season, had a badly-struck penalty saved by Koblenz keeper Dieter Paucken.
The 27-year-old made amends in the second half with a hat-trick in 11 minutes.
Lakic scored twice and Adam Nemec added another as the visitors quickly put the game beyond Koblenz before Lakic slotted home his third in the 65th minute.
Holders Bayern Munich travel to Alemannia Aachen on January 26 and second division Energie Cottbus host Hoffenheim in the other two quarter-finals.