Lisicki, a finalist last summer at Wimbledon, defeated Magdalena Rybarikova 6-3, 6-4 behind a seven-ace attack. She won 69 percent of the points on serve and saved all three break points she faced.
Rybarikova only had to deal with four break chances overall but Lisicki cashed in one in each set to advance.
Andrea Petkovic completed Sunday's schedule with a 6-4, 7-5 decision over Bethanie Mattek-Sands. Petkovic had a pair of breaks in each set and moves into a second-round match against defending champion and world No. 1 Serena Williams.
U.S. players were 0-3 Sunday. In addition to the loss by Mattek-Sands, Elina Svitolina stopped Varvara Lepchenko 6-3, 6-3 by piling up six breaks and Stefanie Voegele dropped her serve just once in getting past Madison Keys 6-4, 6-3.
Also Sunday, Kimiko Date-Krumm used two breaks in each set in beating Olivia Rogowska 6-3, 7-5.
No. 6-seeded Caroline Wozniacki withdrew from the tournament with a right shoulder injury but said she expected to play in next week's event in Sydney, which is the final tune-up before the Australian Open.