Having blown the competition wide open in the quarter-finals by beating reigning champions and eight-times Euro winners Germany 2-1, the Danes looked the better side against an Austria team competing at their first major finals.
Both sides had plenty of chances to score over the 120 minutes, with Austria's Sarah Puntigam missing the best of them as she blasted a penalty high over the bar early in the first half.
Austria had beaten Spain 5-3 on penalties to reach the semis, but this time around they failed to hold their nerve, with Laura Feiersinger missing and Lykke diving to her right to deny both Viktoria Pinther and Verena Aschauer.
Denmark will meet the winner of Thursday's other semi-final between hosts the Netherlands and England in Sunday's final.
(Reporting by Philip O'Connor; Editing by Toby Davis)
