The world number one was tested by the powerful German as she progressed from the night session match in the Australian Open warm-up tournament.
The big-hitting Lisicki blasted her fastest serve at 194km/h as she pinned her opponent back on her own delivery, but crucially she committed 36 unforced errors.
Azarenka will next take on qualifier Ksenia Pervak from Kazakhstan in the quarter-finals, with third seed Serena Williams her likely opponent in the last four.
"I'm such a picky person that I probably never will be satisfied," Azarenka said.
"That's a good thing because I have a lot more matches to play and I can always improve. But it was pretty good. I felt like the things that I've been working on are there. I'm getting into the competitive groove and I'm happy where I'm at right now."
Azarenka faces a challenge to her top ranking from world number two Maria Sharapova and number three Serena Williams when the Australian Open begins at Melbourne Park on January 14.
"I actually don't really look at defending anything - I'm just looking to win," she said.
"I'm going to have the same mindset for as long as I'm playing. That's what I'm looking forward to - improving my game as I always do and match those big challenges, the big players.
"At the beginning of the year, you're obviously hungry to play. The atmosphere here in Australia brings out the best in me. The motivation is always extraordinary. I really like it here."
Heather Watson's singles campaign in Auckland was ended earlier than hoped, the British number one losing a tough three-setter to Dutch player Kiki Bertens.
Having beaten Sorana Cirstea in the opening round, Watson struggled on her second serve and went down 6-4 3-6 6-3 to a player ranked 14 places below her in the world.
Watson will stay on in the New Zealand city to compete in the doubles tournament with Marina Erakovic, while Bertens moves on to meet Jamie Hampton, who beat Erakovic.
Second seed Julia Goerges also stumbled, the German losing lost 5-7 7-6 3-6 to Sweden’s Johanna Larsson.
But there were no problems for tops seed Agnieszka Radwanska, who beat Simona Halep of Romania 6-3 6-1.
There was a relatively comfortable win for top seed Li Na at WTA Shenzhen, meanwhile, as the Chinese player beat Julia Cohen of the USA 6-3 6-4 in their second-round encounter.
WTA Brisbane results
1-Victoria Azarenka (Belarus) beat Sabine Lisicki (Germany) 6-3 6-3
4-Angelique Kerber (Germany) beat Monica Puig (Puerto Rico) 3-6 6-4 7-6(7)
Lesia Tsurenko (Ukraine) beat Jarmila Gajdosova (Australia) 1-6 6-1 6-4
Sloane Stephens (U.S.) beat Sofia Arvidsson (Sweden) 6-3 6-4
WTA Auckland results
1-Agnieszka Radwanska (Poland) beat Simona Halep (Romania) 6-3 6-1
Kiki Bertens (Netherlands) beat Heather Watson (Britain) 6-4 3-6 6-3
Jamie Hampton (U.S.) beat Marina Erakovic (New Zealand) 6-1 7-6(5)
Johanna Larsson (Sweden) beat 2-Julia Goerges (Germany) 7-5 6-7(1) 6-3
Elena Vesnina (Russia) beat 6-Yaroslava Shvedova (Kazakhstan) 6-2 6-3
8-Mona Barthel (Germany) beat Eleni Daniilidou (Greece) 7-6(6) 6-2
Kirsten Flipkens (Belgium) beat Pauline Parmentier (France) 6-2 6-2
3-Yanina Wickmayer (Belgium) beat Romina Oprandi (Switzerland) 6-3 6-0
WTA Shenzhen results
1-Li Na (China) beat Julia Cohen (U.S.) 6-3 6-4
2-Marion Bartoli (France) beat Stefanie Voegele (Switzerland) 7-5 6-4
Zhou Yimiao (China) beat Chang Kai-Chen (Taiwan) 4-6 6-2 7-6(3)