Lisicki notched a straight-set victory over American Madison Keys 7-5, 6-3 to advance to the second round of the U.S. National Indoor Tennis Championships.
The result wasn't as good for Hradecka, however, as she was upended by French qualifier Claire Feuerstein 6-3, 6-4.
Another first-round win was posted by the Czech Republic's Andrea Hlavackova, who dispatched American Melanie Oudin 6-4, 3-6, 6-3.
In second-round play Tuesday, No. 7 seed Magdalena Rybarikova of Slovakia reached the quarterfinals with a 7-6 (7-2), 6-2 triumph over American Lauren Davis.
Joining her in the quarters was Jamie Hampton, who breezed past American Coco Vandeweghe 6-3, 6-0.