Three clinical finishes from Olic - one right-foot shot, a left-foot shot and a header - helped the four-times European champions complete a 4-0 aggregate semi-final success to silence the vocal faithful at Stade Gerland.
Olic netted his first after 26 minutes with a neat turn and shot, smashed in a pass from Hamit Altintop after 67 minutes and completed his hat-trick with a header 12 minutes from time.
It was only the second hat-trick in a Champions League semi-final after Alessandro Del Piero's treble for Juventus against Monaco in 1998.
"I didn't think we'd win in such a one-sided manner and that I'd get three goals," Olic told German TV. "That's just incredible in a match like this."
"We had a great game, we were well positioned on the pitch and if we play like this all the way, it will be hard to beat us", Bayern's Dutch coach Louis van Gaal told a news conference.
"The players now know what it's like to spend 10 months with Van Gaal, they know it's not easy but they're happy now and so am I."
Lyon finished the game with 10 men after centre back Cris was sent off just before the hour. He was booked for a foul on Olic, then shown a second yellow card for mocking referee Massimo Busacca's decision.
"They were the stronger team. Too bad we failed to equalise (after the first goal) because we had a few chances," Lyon coach Claude Puel told French TV channel TF1.
