Lisicki had no trouble with the Slovakian or the 42 degrees Celsius heat on Pat Rafter Arena, winning 6-3, 6-4 in 89 minutes.
Lisicki was never in any trouble against Rybarikova and now meets Swiss player Stefanie Voegele in the second round.
Voegele progressed when she beat American Madison Keys 6-4, 6-3.
Meanwhile, Japan’s evergreen 43-year-old Kimiko Date-Krumm defeated wildcard Olivia Rogowska 6-3, 7-5, while Elina Svitolina beat Varvara Lepchenko 6-3, 6-3.
Photos: Kareena Kapoor Khan and Aamir Khan at Mumbai airport
Photos: SRK, wife Gauri, Aishwarya Rai, Shweta Bachchan at Vogue Awards
Photos: Harbhajan Singh-Geeta Basra's TV outing with daughter Hinaya
Photos: Malaika Arora flaunts ripped jeans like a boss!
Photos: Vaani Kapoor, Kriti Sanon, Dia Mirza sizzle on the ramp