Shnaider, ranked No 14 and a three-time WTA title winner this year, scored her 40th match win of the season. She will face the winner of the match between Canadian Leylah Fernandez, the No 3 seed, and American Bernarda Pera, the No 9 seed, next.
The 20-year-old Russian won against Japanese qualifier Kyoka Okamura (6-3, 6-3) and Australian Priscilla Hon (6-4, 6-1) in the previous rounds of the tournament. She also improves to 9-1 in WTA Tour level quarter-finals.
Earlier in the week, Lamens, who won the Osaka title last month and is now ranked No 91, beat Chinese qualifier Xinyu Gao (6-3, 6-0) and Spaniard Cristina Bucsa, the No 8 seed (5-7, 6-4, 6-3).
Hong Kong WTA 250, other quarter-final matches (Victoria Park, Causeway Bay, hard, USD 267,082):
