Shnaider saved all three break points she faced and benefited from four double faults by her foe to dispatch Lys in one hour and 25 minutes.
Shnaider will bid for her third title of the year on Sunday when she faces unseeded Belarus native Aliaksandra Sasnovich (30), who rallied to a 6-3, 3-6, 7-5 win over Anna Karolina Schmiedlova (29) of Slovakia.
Sasnovich overcame 17 double faults and bounced back from a 5-2 deficit in the third set to jolt Schmiedlova in two hours and 46 minutes.
Follow the Budapest final on Flashscore.
Palermo Ladies Open
Top-seeded Qinwen Zheng (21) of China recorded a 7-5, 6-4 semifinal victory over fourth-seeded Diane Parry (21) of France to reach the final in Italy.
Zheng will face second-seeded Karolina Muchova (27) of the Czech Republic in the championship match. Zheng is the defending champ.
Zheng saved three of four break points and won 84.8 per cent (28 of 33) of her first-serve points. Parry saved two of five break points and won 69.4 per cent (25 of 36) of her first-serve points.
Muchova defeated Romania's Irina-Camelia Begu (33) 6-1, 6-1 in her semi-final match. Muchova had a 4-0 edge in aces over Begu, the 2022 champion.
