Alcaraz reaches first quarter-final on grass at Queen's Club
Alcaraz is competing at Queen's for the first time and the Spanish star is gradually finding his footing on the lawns of west London.
The 20-year-old routed Lehecka 6-2, 6-3 as he improved on a laboured first round win over Arthur Rinderknech.
Alcaraz won the US Open last year and reached the French Open semi-finals earlier in June, losing to eventual champion Novak Djokovic on the Paris clay.
Yet to go past the Wimbledon last 16, Alcaraz believes he is making strides at just the right time, with the All England Club tournament starting on July 3.
"I'll enjoy my first quarter-final, it's a beautiful place to play and I'm enjoying every second here," Alcaraz said.
"It's more practice and I am happy getting experience on grass. After this match the expectation changes. I think I'm ready to get a good result on grass."
Top seeded Alcaraz will face former Queen's champion Grigor Dimitrov in the quarter-finals on Friday after the Bulgarian defeated Francisco Cerundolo 6-3, 7-5.
Andy Murray's first round conqueror Alex De Minaur defeated Diego Schwartzman 6-2, 6-2 to book a quarter-final against France's Adrian Mannarino, who beat Taylor Fritz 6-4, 7-6 (9/7).
British number one Cameron Norrie meets American Sebastian Korda in the last eight.
Norrie will have plenty of attention as the last Briton in the tournament, but the 27-year-old says he would not enjoy the unrelenting spotlight of the recent Netflix tennis documentary Break Point.
Nick Kyrgios, Matteo Berrettini and Fritz were among the players followed by the Break Point cameras.
"For me it's more important to keep training as hard as I can and to be known for being a tennis player and a good competitor," Norrie said.
The former Wimbledon semi-finalist added: "I think it's a big distraction having the cameraman there full time.
"I probably wouldn't do it, but that's me right now. I can understand why some players fancy it and why they are choosing the players that they are."