1 seed Andrey Rublev 4-6, 6-4, 6-3 in the quarterfinals of the Qatar ExxonMobil Open on Thursday in Doha.
Lehecka will face Great Britain's Andy Murray in the semifinals after Murray rallied past French qualifier Alexandre Muller 4-6, 6-1, 6-2.
7 seed Alejandro Davidovich Fokina 6-4, 7-6 (5) on Thursday while Medvedev battled past Christopher O'Connell of Australia 6-2, 4-6, 7-5.
1 seed Hubert Hurkacz of Poland dropped his first set before rallying past Switzerland's Leandro Riedi 4-6, 6-3, 6-2 in second-round action at Marseille, France.
Third seed Alex de Minaur of Australia beat Swiss qualifier Alexander Ritschard 6-3, 6-3, while fourth seed Grigor Dimitrov of Bulgaria was a 6-3, 6-2 winner over Dutch qualifier Gijs Brouwer.