The match is scheduled for Thursday, at 11:30 a.m. local time in New York (5:30 p.m. in Poland).
Świątek, the 2022 US Open champion, advanced comfortably in her opening match, defeating Colombian Emiliana Arango 6-1, 6-2.
Lamens, 26, a Dutch player, reached the second round after beating American Valerie Glozman 6-4, 6-2.
A win could put Świątek back on course for the top spot in the WTA rankings if current world number one Aryna Sabalenka is eliminated before the quarter-finals.
Other leading players, including world number three Coco Gauff, are also competing this week, with Gauff set to face Australia’s Ajla Tomljanovic.
Last year, Świątek was eliminated in the quarter-finals.
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Source: Sport/PR24/X/@IgaUpdates_/@sport_pr24pl