Lisicki, the second seed, won 7-5 7-6 (7/1) and next meets Polona Hercog, a three-set winner over Petra Cetkovska.
Fourth seed Flavia Pennetta, who reached the semi-finals at the US Open, was the biggest casualty of round one, going down 3-5 7-5 6-0 to Vania King.
Seventh seed Laura Robson also lost, 6-4 6-4 to 43-year-old Kimiko Date-Krumm, but sixth seed Maidson Keys and ninth seed Kristina Mladenovic are through.
There was another impressive win, meanwhile, for Swiss teenager Belinda Bencic, who beat Lauren Davis 6-3 7-5.
The 16-year-old, who won the junior titles at the French Open and Wimbledon this year, is coached by Martina Hingis' mother Melanie Molitor.
There were also victories for Chinese pair Zheng Jie and Zhang Shuai and qualifiers Luksika Kumkhum and Barbora Zahlavova Strycova.